Abstract: Lead-halide-based perovskites have been the subject of numerous recent studies largely motivated by their exceptional performance in solar cells. Electronic and optical properties of these materials have been commonly controlled by varying the composition (e.g., the halide component) and/or crystal structure. Use of nanostructured forms of perovskites can provide additional means for tailoring their functionalities via effects of quantum confinement and wave function engineering. Furthermore, it may enable applications that explicitly rely on the quantum nature of electronic excitations. Here, we demonstrate that CsPbX3 quantum dots (X = I, Br) can serve as room-temperature sources of quantum light, as indicated by strong photon antibunching detected in single-dot photoluminescence measurements. We explain this observation by the presence of fast nonradiative Auger recombination, which renders multiexciton states virtually nonemissive and limits the fraction of photon coincidence events to ∼6% on average....

Abstract: We show that the spectral weights W mK (k ) used for the unfolding of two-component spinor eigenstates ∣ ∣ ψ SC mK ⟩=|α⟩|ψ SC mK ,α⟩+|β⟩|ψ SC mK ,β⟩ can be decomposed as the sum of the pa ...

Abstract: Quantum magnets have occupied the fertile ground between many-body theory and low-temperature experiments on real materials since the early days of quantum mechanics. However, our understanding of even deceptively simple systems of interacting spins-1/2 is far from complete. The quantum square-lattice Heisenberg antiferromagnet (QSLHAF), for example, exhibits a striking anomaly of hitherto unknown origin in its magnetic excitation spectrum. This quantum effect manifests itself for excitations propagating with the specific wave vector (π, 0). We use polarized neutron spectroscopy to fully characterize the magnetic fluctuations in the metal-organic compound CFTD, a known realization of the QSLHAF model. Our experiments reveal an isotropic excitation continuum at the anomaly, which we analyse theoretically using Gutzwiller-projected trial wavefunctions. The excitation continuum is accounted for by the existence of spatially-extended pairs of fractional S=1/2 quasiparticles, 2D analogues of 1D spinons. Away from the anomalous wave vector, these fractional excitations are bound and form conventional magnons. Our results establish the existence of fractional quasiparticles in the high-energy spectrum of a quasi-two-dimensional antiferromagnet, even in the absence of frustration.

Abstract: The treatment of high-dimensional problems such as the Schrodinger equation can be approached by concepts of tensor product approximation. We present general techniques that can be used for the treatment of high-dimensional optimization tasks and time-dependent equations, and connect them to concepts already used in many-body quantum physics. Based on achievements from the past decade, entanglement-based methods—developed from different perspectives for different purposes in distinct communities already matured to provide a variety of tools—can be combined to attack highly challenging problems in quantum chemistry. The aim of the present paper is to give a pedagogical introduction to the theoretical background of this novel field and demonstrate the underlying benefits through numerical applications on a text book example. Among the various optimization tasks, we will discuss only those which are connected to a controlled manipulation of the entanglement which is in fact the key ingredient of the methods considered in the paper. The selected topics will be covered according to a series of lectures given on the topic “New wavefunction methods and entanglement optimizations in quantum chemistry” at the Workshop on Theoretical Chemistry, February 18–21, 2014, Mariapfarr, Austria. © 2015 Wiley Periodicals, Inc.

Abstract: We present a novel quantum-classical approach to nonadiabatic dynamics, deduced from the coupled electronic and nuclear equations in the framework of the exact factorization of the electron-nuclear wave function. The method is based on the quasiclassical interpretation of the nuclear wave function, whose phase is related to the classical momentum and whose density is represented in terms of classical trajectories. In this approximation, electronic decoherence is naturally induced as an effect of the coupling to the nuclei and correctly reproduces the expected quantum behavior. Moreover, the splitting of the nuclear wave packet is captured as a consequence of the correct approximation of the time-dependent potential of the theory. This new approach offers a clear improvement over Ehrenfest-like dynamics. The theoretical derivation presented in this Letter is supported by numerical results that are compared to quantum mechanical calculations.

Abstract: This report on progress explores recent advances in our theoretical and experimental understanding of the physics of open quantum systems (OQSs). The study of such systems represents a core problem in modern physics that has evolved to assume an unprecedented interdisciplinary character. OQSs consist of some localized, microscopic, region that is coupled to an external environment by means of an appropriate interaction. Examples of such systems may be found in numerous areas of physics, including atomic and nuclear physics, photonics, biophysics, and mesoscopic physics. It is the latter area that provides the main focus of this review, an emphasis that is driven by the capacity that exists to subject mesoscopic devices to unprecedented control. We thus provide a detailed discussion of the behavior of mesoscopic devices (and other OQSs) in terms of the projection-operator formalism, according to which the system under study is considered to be comprised of a localized region (Q), embedded into a well-defined environment (P) of scattering wavefunctions (with Q + P = 1). The Q subspace must be treated using the concepts of non-Hermitian physics, and of particular interest here is: the capacity of the environment to mediate a coupling between the different states of Q; the role played by the presence of exceptional points (EPs) in the spectra of OQSs; the influence of EPs on the rigidity of the wavefunction phases, and; the ability of EPs to initiate a dynamical phase transition (DPT). EPs are singular points in the continuum, at which two resonance states coalesce, that is where they exhibit a non-avoided crossing. DPTs occur when the quantum dynamics of the open system causes transitions between non-analytically connected states, as a function of some external control parameter. Much like conventional phase transitions, the behavior of the system on one side of the DPT does not serve as a reliable indicator of that on the other. In addition to discussing experiments on mesoscopic quantum point contacts that provide evidence of the environmentally-mediated coupling of quantum states, we also review manifestations of DPTs in mesoscopic devices and other systems. These experiments include observations of resonance-trapping behavior in microwave cavities and open quantum dots, phase lapses in tunneling through single-electron transistors, and spin swapping in atomic ensembles. Other possible manifestations of this phenomenon are presented, including various superradiant phenomena in low-dimensional semiconductors. From these discussions a generic picture of OQSs emerges in which the environmentally-mediated coupling between different quantum states plays a critical role in governing the system behavior. The ability to control or manipulate this interaction may even lead to new applications in photonics and electronics.

Abstract: These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrodinger dynamics in certain physically interesting regimes. The focus is primarily on the derivation of time-dependent effective theories (non-equilibrium question) approximating many-body quantum dynamics. The book is divided into seven sections, the first of which briefly reviews the main properties of many-body quantum systems and their time evolution. Section 2 introduces the mean-field regime for bosonic systems and explains how the many-body dynamics can be approximated in this limit using the Hartree equation. Section 3 presents a method, based on the use of coherent states, for rigorously proving the convergence towards the Hartree dynamics, while the fluctuations around the Hartree equation are considered in Section 4. Section 5 focuses on a discussion of a more subtle regime, in which the many-body evolution can be approximated by means of the nonlinear Gross-Pitaevskii equation. Section 6 addresses fermionic systems (characterized by antisymmetric wave functions); here, the fermionic mean-field regime is naturally linked with a semiclassical regime, and it is proven that the evolution of approximate Slater determinants can be approximated using the nonlinear Hartree-Fock equation. In closing, Section 7 reexamines the same fermionic mean-field regime, but with a focus on mixed quasi-free initial data approximating thermal states at positive temperature.

Abstract: The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion.

Abstract: We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition We present the first application of a recently developed technique for simulating Hamiltonian evolution using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision, an exponential improvement over all prior methods The two algorithms developed in this work rely on a second quantized encoding of the wavefunction in which the state of an $N$ spin-orbital system is encoded in ${\cal O}(N)$ qubits Our first algorithm requires at most $\widetilde{\cal O}(N^8 t)$ gates Our second algorithm involves on-the-fly computation of molecular integrals, in a way that is exponentially more precise than classical sampling methods, by using the truncated Taylor series simulation technique Our second algorithm has the lowest gate count of any approach to second quantized quantum chemistry simulation in the literature, scaling as $\widetilde{\cal O}(N^{5} t)$ The approaches presented here are readily applicable to a wide class of fermionic models, many of which are defined by simplified versions of the chemistry Hamiltonian

Abstract: Quantum mechanics exhibit many unusual features, including Einstein’s so-called ‘spooky action at a distance’, wherein a wavefunction collapses at all points except where it is detected. Using homodyne measurements, Fuwa et al. verify this effect for a single photon split between two labs.

Abstract: We study the dynamic response of an s-wave BCS-BEC (atomic-molecular) condensate to detuning quenches within the two channel model beyond the weak coupling BCS limit. At long times after the quench, the condensate ends up in one of three main asymptotic states (nonequilibrium phases), which are qualitatively similar to those in other fermionic condensates defined by a global complex order parameter. In phase I the amplitude of the order parameter vanishes as a power law, in phase II it goes to a nonzero constant, and in phase III it oscillates persistently. We construct exact quench phase diagrams that predict the asymptotic state (including the many-body wavefunction) depending on the initial and final detunings and on the Feshbach resonance width. Outside of the weak coupling regime, both the mechanism and the time dependence of the relaxation of the amplitude of the order parameter in phases I and II are modified. Also, quenches from arbitrarily weak initial to sufficiently strong final coupling do not produce persistent oscillations in contrast to the behavior in the BCS regime. The most remarkable feature of coherent condensate dynamics in various fermion superfluids is an effective reduction in the number of dynamic degrees of freedom as the evolution time goes to infinity. As a result, the long time dynamics can be fully described in terms of just a few new collective dynamical variables governed by the same Hamiltonian only with "renormalized" parameters. Combining this feature with the integrability of the underlying (e.g. the two channel) model, we develop and consistently present a general method that explicitly obtains the exact asymptotic state of the system.

Abstract: By quantizing the semiclassical motion of excitons, we show that the Berry curvature can cause an energy splitting between exciton states with opposite angular momentum. This splitting is determined by the Berry curvature flux through the k-space area spanned by the relative motion of the electron-hole pair in the exciton wave function. Using the gapped two-dimensional Dirac equation as a model, we show that this splitting can be understood as an effective spin-orbit coupling effect. In addition, there is also an energy shift caused by other "relativistic" terms. Our result reveals the limitation of the venerable hydrogenic model of excitons, and it highlights the importance of the Berry curvature in the effective mass approximation.

Abstract: Exact calculations are performed on the two-dimensional strongly interacting unpolarized uniform Fermi gas with a zero-range attractive interaction. Two auxiliary-field approaches are employed which accelerate the sampling of imaginary-time paths using BCS trial wave functions and a force bias technique. Their combination enables calculations on large enough lattices to reliably compute ground-state properties in the thermodynamic limit. An equation of state is obtained with a parametrization provided, which can serve as a benchmark and allow accurate comparisons with experiments. The pressure, contact parameter, and condensate fraction are determined systematically vs ${k}_{F}a$. The momentum distribution, pairing correlation, and the structure of the pair wave function are computed. The use of force bias to accelerate the Metropolis sampling of auxiliary fields in determinantal approaches is discussed.

Abstract: We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.

Abstract: We present the exact solution of the stationary Schrodinger equation for the potential . Each of the two fundamental solutions that compose the general solution of the problem is given by a combination with non-constant coefficients of two confluent hypergeometric functions of a shifted argument. Alternatively, the solution is written through the first derivative of a tri-confluent Heun function. Apart from the quasi-polynomial solutions provided by the energy specification , we discuss the bound-state wave functions vanishing both at infinity and in the origin. The exact spectrum equation involves two Hermite functions of non-integer order which are not polynomials. An accurate approximation for the spectrum providing a relative error less than 10−3 is . Each of the wave functions of bound states in general involves a combination with non-constant coefficients of two confluent hypergeometric and two non-integer order Hermite functions of a scaled and shifted coordinate.

Abstract: Interesting non-Abelian states, e.g., the Moore-Read Pfaffian and the anti-Pfaffian, offer candidate descriptions of the $ u = 5/2$ fractional quantum Hall state. But the significant controversy surrounding the nature of the $ u = 5/2$ state has been hampered by the fact that the competition between these and other states is affected by small parameter changes. To study the phase diagram of the $ u = 5/2$ state we numerically diagonalize a comprehensive effective Hamiltonian describing the fractional quantum Hall effect of electrons under realistic conditions in GaAs semiconductors. The effective Hamiltonian takes Landau level mixing into account to lowest-order perturbatively in $\kappa$, the ratio of the Coulomb energy scale to the cyclotron gap. We also incorporate non-zero width $w$ of the quantum well and sub-band mixing. We find the ground state in both the torus and spherical geometries as a function of $\kappa$ and $w$. To sort out the non-trivial competition between candidate ground states we analyze the following 4 criteria: its overlap with trial wave functions; the magnitude of energy gaps; the sign of the expectation value of an order parameter for particle-hole symmetry breaking; and the entanglement spectrum. We conclude that the ground state is in the universality class of the Moore-Read Pfaffian state, rather than the anti-Pfaffian, for $\kappa < {\kappa_c}(w)$, where ${\kappa_c}(w)$ is a $w$-dependent critical value $0.6 \lesssim{\kappa_c}(w)\lesssim 1$. We observe that both Landau level mixing and non-zero width suppress the excitation gap, but Landau level mixing has a larger effect in this regard. Our findings have important implications for the identification of non-Abelian fractional quantum Hall states.

Abstract: The formation of bound states involving multiple particles underlies many interesting quantum physical phenomena, such as Efimov physics or superconductivity. In this work we show the existence of an infinite number of such states for some boson impurity models. They describe free bosons coupled to an impurity and include some of the most representative models in quantum optics. We also propose a family of wavefunctions to describe the bound states and verify that it accurately characterizes all parameter regimes by comparing its predictions with exact numerical calculations for a one-dimensional tight-binding Hamiltonian. For that model, we also analyze the nature of the bound states by studying the scaling relations of physical quantities such as the ground state energy and localization length, and find a non-analytical behavior as a function of the coupling strength. Finally, we discuss how to test our theoretical predictions in experimental platforms such as photonic crystal structures and cold atoms in optical lattices.

Abstract: Although liquid water is ubiquitous in chemical reactions at roots of life and climate on the earth, the prediction of its properties by high-level ab initio molecular dynamics simulations still represents a formidable task for quantum chemistry. In this article, we present a room temperature simulation of liquid water based on the potential energy surface obtained by a many-body wave function through quantum Monte Carlo (QMC) methods. The simulated properties are in good agreement with recent neutron scattering and X-ray experiments, particularly concerning the position of the oxygen-oxygen peak in the radial distribution function, at variance of previous density functional theory attempts. Given the excellent performances of QMC on large scale supercomputers, this work opens new perspectives for predictive and reliable ab initio simulations of complex chemical systems.

Abstract: We develop a theoretical framework to investigate the two-body composite structure of a resonance as well as a bound state from its wave function. For this purpose, we introduce both one-body bare states and two-body scattering states, and define the compositeness as a fraction of the contribution of the two-body wave function to the normalization of the total wave function. Writing down explicitly the wave function for a resonance state obtained with a general separable interaction, we formulate the compositeness in terms of the position of the resonance pole, the residue of the scattering amplitude at the pole, and the derivative of the Green function of the free two-body scattering system. At the same time, our formulation provides the elementariness expressed with the resonance properties and the two-body effective interaction, and confirms the sum rule showing that the summation of the compositeness and elementariness gives unity. In this formulation, Weinberg's relation for the scattering length and effective range can be derived in the weak binding limit. The extension to the resonance states is performed with the Gamow vector, and a relativistic formulation is also established. As its applications, we study the compositeness of the $\Lambda (1405)$ resonance and the light scalar and vector mesons described with refined amplitudes in coupled-channel models with interactions up to the next-to-leading order in chiral perturbation theory. We find that $\Lambda (1405)$ and $f_{0}(980)$ are dominated by the $\bar {K} N$ and $K \bar {K}$ composite states, respectively, while the vector mesons $\rho (770)$ and $K^{\ast } (892)$ are elementary. We also briefly discuss the compositeness of $N (1535)$ and $\Lambda (1670)$ obtained in a leading-order chiral unitary approach.

Abstract: The accurate and efficient description of strongly correlated systems remains an important challenge for computational methods. Doubly occupied configuration interaction (DOCI), in which all electrons are paired and no correlations which break these pairs are permitted, can in many cases provide an accurate account of strong correlations, albeit at combinatorial computational cost. Recently, there has been significant interest in a method we refer to as pair coupled cluster doubles (pCCD), a variant of coupled cluster doubles in which the electrons are paired. This is simply because pCCD provides energies nearly identical to those of DOCI, but at mean-field computational cost (disregarding the cost of the two-electron integral transformation). Here, we introduce the more complete pair extended coupled cluster doubles (pECCD) approach which, like pCCD, has mean-field cost and reproduces DOCI energetically. We show that unlike pCCD, pECCD also reproduces the DOCI wave function with high accuracy. Moreover, pECCD yields sensible albeit inexact results even for attractive interactions where pCCD breaks down.

Abstract: An implementation of coupled-cluster (CC) theory to treat atoms and molecules in finite magnetic fields is presented. The main challenges for the implementation stem from the magnetic-field dependence in the Hamiltonian, or, more precisely, the appearance of the angular momentum operator, due to which the wave function becomes complex and which introduces a gauge-origin dependence. For this reason, an implementation of a complex CC code is required together with the use of gauge-including atomic orbitals to ensure gauge-origin independence. Results of coupled-cluster singles–doubles–perturbative-triples (CCSD(T)) calculations are presented for atoms and molecules with a focus on the dependence of correlation and binding energies on the magnetic field.

Abstract: The nuclear velocity perturbation theory (NVPT) for vibrational circular dichroism (VCD) is derived from the exact factorization of the electron-nuclear wave function. This new formalism offers an exact starting point to include correction terms to the Born-Oppenheimer (BO) form of the molecular wave function, similar to the complete-adiabatic approximation. The corrections depend on a small parameter that, in a classical treatment of the nuclei, is identified as the nuclear velocity. Apart from proposing a rigorous basis for the NVPT, we show that the rotational strengths, related to the intensity of the VCD signal, contain a new contribution beyond-BO that can be evaluated with the NVPT and that only arises when the exact factorization approach is employed. Numerical results are presented for chiral and non-chiral systems to test the validity of the approach.

Abstract: The energies of the canonical (standard, amino-keto) and tautomeric (non-standard, imino-enol) charge-neutral forms of the adenine–thymine base pair (A–T and A*–T*, respectively) are calculated using density functional theory. The reaction pathway is then computed using a transition state search to provide the asymmetric double-well potential minima along with the barrier height and shape, which are combined to create the potential energy surface using a polynomial fit. The influence of quantum tunnelling on proton transfer within a base pair H-bond (modelled as the DFT deduced double-well potential) is then investigated by solving the time-dependent master equation for the density matrix. The effect on a quantum system by its surrounding water molecules is explored via the inclusion of a dissipative Lindblad term in the master equation, in which the environment is modelled as a heat bath of harmonic oscillators. It is found that quantum tunnelling, due to transitions to higher energy eigenstates with significant amplitudes in the shallow (tautomeric) side of the potential, is unlikely to be a significant mechanism for the creation of adenine–thymine tautomers within DNA, with thermally assisted coupling of the environment only able to boost the tunnelling probability to a maximum of 2 × 10−9. This is barely increased for different choices of the starting wave function or when the geometry of the potential energy surface is varied.

Abstract: We study possible quantum $U(1)$ spin liquids in three dimensions with time-reversal symmetry. We find a total of 7 families of such $U(1)$ spin liquids, distinguished by the properties of their emergent electric/magnetic charges. We show how these spin liquids are related to each other. Two of these classes admit nontrivial protected surface states which we describe. We show how to access all of the 7 spin liquids through slave particle (parton) constructions. We also provide intuitive loop gas descriptions of their ground state wave functions. One of these phases is the `topological Mott insulator' conventionally described as a topological insulator of an emergent fermionic `spinon'. We show that this phase admits a remarkable dual description as a topological insulator of emergent fermionic magnetic monopoles. This results in a new (possibly natural) surface phase for the topological Mott insulator and a new slave particle construction. We describe some of the continuous quantum phase transitions between the different $U(1)$ spin liquids. Each of these seven families of states admits a finer distinction in terms of their surface properties which we determine by combining these spin liquids with symmetry protected topological phases. We discuss lessons for materials such as pyrochlore quantum spin ices which may harbor a $U(1)$ spin liquid. We suggest the topological Mott insulator as a possible ground state in some range of parameters for the quantum spin ice Hamiltonian.

Abstract: A method for diabatising multiple electronic states on-the-fly within the direct dynamics variational multi-configuration Gaussian method for calculating quantum nuclear dynamics is presented. The method is based upon the propagation of the adiabatic-diabatic transformation matrix along the paths followed by the Gaussian basis functions that constitute the nuclear wave function, by use of a well-known differential equation relating the matrix and the nonadiabatic vector coupling terms between the electronic states. The implementation of the method is described, and test calculations are presented using the ground and first-excited states of the butatriene cation as an example, allowing comparison to the earlier regularisation diabatisation scheme as well as to full nuclear dynamics on a precomputed potential energy surface. The new scheme is termed propagation diabatisation.