Class Of Variational Wave Functions Research Articles

Neural network evolution strategy for solving quantum sign structures

Feed-forward neural networks are a novel class of variational wave functions for correlated many-body quantum systems. Here, we propose a specific neural network ansatz suitable for systems with real-valued wave functions. Its characteristic is to encode the all-important rugged sign structure of a quantum wave function in a convolutional neural network with discrete output. Its training is achieved through an evolutionary algorithm. We test our variational ansatz and training strategy on two spin-1/2 Heisenberg models, one on the two-dimensional square lattice and one on the three-dimensional pyrochlore lattice. In the former, our ansatz converges with high accuracy to the analytically known sign structures of ordered phases. In the latter, where such sign structures are a priory unknown, we obtain better variational energies than with other neural network states. Our results demonstrate the utility of discrete neural networks to solve quantum many-body problems.

A Variational Approach to London Dispersion Interactions without Density Distortion.

We introduce a class of variational wave functions that captures the long-range interaction between neutral systems (atoms and molecules) without changing the diagonal of the density matrix of each monomer. The corresponding energy optimization yields explicit expressions for the dispersion coefficients in terms of the ground-state pair densities of the isolated systems, providing a clean theoretical framework to build new approximations in several contexts. As the individual monomer densities are kept fixed, we can also unambiguously assess the effect of the density distortion on London dispersion interactions; for example, we obtain virtually exact dispersion coefficients between two hydrogen atoms up to C10 and relative errors below 0.2% in other simple cases.

Variational study of polarons in Bose-Einstein condensates

We use a class of variational wave functions to study the properties of an impurity in a Bose-Einstein condensate, i.e., the Bose polaron. The impurity interacts with the condensate through a contact interaction, which can be tuned by a Feshbach resonance. We find a stable attractive polaron branch that evolves continuously across the resonance to a tight-binding diatomic molecule deep in the positive scattering length side. A repulsive polaron branch with finite lifetime is also observed and it becomes unstable as the interaction strength increases. The effective mass of the attractive polaron also changes smoothly across the resonance connecting the two well-understood limits deep on both sides.

Variational Monte Carlo approach to the two-dimensional Kondo lattice model

We study the phase diagram of the Kondo lattice model with nearest-neighbor hopping in the square lattice by means of the variational Monte Carlo technique. Specifically, we analyze a wide class of variational wave functions that allow magnetic and superconducting order parameters, so as to assess the possibility that superconductivity might emerge close to the magnetic instability, as is often observed in heavy-fermion systems. Indeed, we do find evidence of $d$-wave superconductivity in the paramagnetic sector, i.e., when magnetic order is not allowed in the variational wave function. However, when magnetism is allowed, it completely covers the superconducting region, which thus disappears from the phase diagram.

From Luttinger liquid to Mott insulator: The correct low-energy description of the one-dimensional Hubbard model by an unbiased variational approach

We show that a particular class of variational wave functions reproduces the low-energy properties of the Hubbard model in one dimension. Our approach generalizes to finite on-site Coulomb repulsion the fully-projected wave function proposed by Hellberg and Mele [Phys. Rev. Lett. {\bf 67}, 2080 (1991)] for describing the Luttinger-liquid behavior of the doped $t{-}J$ model. Within our approach, the long-range Jastrow factor emerges from a careful minimization of the energy, without assuming any parametric form for the long-distance tail. Specifically, in the conducting phase of the Hubbard model at finite hole doping, we obtain the correct power-law behavior of the correlation functions, with the exponents predicted by the Tomonaga-Luttinger theory. By decreasing the doping, the insulating phase is reached with a continuous change of the small-$q$ part of the Jastrow factor.

Superfluidity or supersolidity as a consequence of off-diagonal long-range order

We present a general derivation of Hess-Fairbank effect or nonclassical rotational inertial (NCRI), i.e., the refusal to rotate with its container, as well as the quantization of angular momentum, as consequences of off-diagonal long-range order (ODLRO) in an interacting Bose system. Afterwards, the path integral formulation of superfluid density is rederived without ignoring the centrifugal potential. Finally and in particular, for a class of variational wave functions used for solid helium, treating the constraint of single-valuedness boundary condition carefully, we show that there is no ODLRO and, especially, demonstrate explicitly that NCRI cannot be possessed in absence of defects, even though there exist zero-point motion and exchange effect.

Thecoherent-state wave function for solid 3He

A new class of variational wave functions describing many-bodysystems with spin-dependent correlations is used to study solid3He. The idea of spin coherent states is used to construct avariational coherent-state wave function for solid 3He as anantisymmetrized Jastrow-Nosanow wave function that also containsspin-dependent correlations. We investigate this wave function by avariational Monte Carlo method. The addition of triplet(three-body) correlations produces a ground-state energy perparticle that is a considerable improvement upon other variationalresults, but still appreciable discrepancies with the experimentremain. We speculate that such discrepancies point to anon-negligible effect of more-than-three-body correlations for bothliquid and solid 3He.

Superconductivity from repulsion: a variational view

This work present a new class of variational wave functions for fermi systems in any dimension. These wave functions introduce correlations between Cooper pairs in different momentum states and the relevant correlations can be computed analytically. At half filling we have a ground state with critical superconducting correlations, that is argued to be exact for the model considered. We find large enhancements in a Cooper pair correlation function caused purely by the interplay between the uncertainty principle, repulsion and the proximity of half filling. This is surprising since there is no accompanying signature in usual charge and spin response functions, and typifies a novel kind of many body cooperative behaviour.

Quantum Numbers of Textured Hall Effect Quasiparticles.

We propose a class of variational wave functions with slow variation in spin and charge density and simple vortex structure at infinity, which properly generalize both the Laughlin quasiparticles and baby Skyrmions. We argue that the spin of the corresponding quasiparticle has a fractional part related in a universal fashion to the properties of the bulk state, and propose a direct experimental test of this claim. We show that certain spin-singlet quantum Hall states can be understood as arising from primary polarized states by Skyrmion condensation.

Generalized dimer states

We present a new class of variational wavefunctions that can be used to investigate quantum antiferromagnetic systems. The states are a natural generalization of the nearest-neighbour dimer phases which have been thoroughly studied in the literature. We describe a one-dimensional class of total-spin-singlet wavefunctions, which include as special cases the two nearest-neighbour dimer phases and the exact solution to the total-spin-two projector Hamiltonian. These different solutions are 'smoothly' interpolated by a range of singlets with short-range correlations. Although the states have only short-range order, we can obtain over 98% of the ground-state energy of the nearest-neighbour Heisenberg model. We apply our basis to the J1-J2 Heisenberg model and the single hole in the t1-t2 infinite-U Hubbard model, successfully predicting the behaviour observed in finite-size scaling calculations.

Phase diagram of the one-dimensional t-J model from variational theory.

We study a class of variational wave functions for strongly interacting one-dimensional lattice fermions in which correlations among the particles are specified by a single variational parameter. We find that the wave functions describe the ground-state properties of the one-dimensional t-J model remarkably well over the entire phase diagram in which interaction strength and density are varied. Specifically the wave function describes a Tomonaga-Luttinger liquid at low J/t, a phase-separated state at large J/t, and a stable state with infinite compressibility between these phases at low densities.

Composite-fermion theory for the strongly correlated Hubbard model.

We study a class of variational wave functions for strongly correlated systems by expanding the electron operators as composites of spin-1/2 Fermi fields and spinless Fermi fields. The composite particles automatically satisfy the local constraint of no double occupancy and include correlations between opposite-spin particles in a very physical way. We calculate the energy and correlation functions for the one-dimensional U=\ensuremath{\infty} Hubbard model, where a comparison with exact results is made. The method is computationally very tractable and can readily be generalized to higher dimensions.

Variational Many Body States for the U=∞ Hubbard Model

We study a general class of variational wavefunctions for strongly correlated lattice fermions. The wavefunctions considered here automatically satisfy local constraints of no double occupancy and include correlations between opposite spin particles in a very physical way. We calculate the energy and correlation functions for the one dimensional U=∞ Hubbard model, where a comparison with exact results is made. We briefly report on preliminary results for the t-J model.

Commensurate-flux-phase state of the t-J model.

We propose a variational approach for the study of chiral flux-phase states. We present a class of variational wave functions of the generalized Laughlin-type. The generalization consists of the introduction of Gutzwiller projections and of a fictitious magnetic field. We classify antiferromagnetic chiral flux-phase states and evaluate analytically the corresponding expectation values of the t-J Hamiltonian at any value of filling. There are two types of chiral flux-phase states: commensurate and fractional. We have found that the minimal energy has a commensurate-flux-phase state for which the value of the flux of the orbital magnetic field equals the filling.

Shadow wave-function variational calculations of crystalline and liquid phases of 4He.

A new class of variational wave functions for boson systems, shadow wave functions, is used to investigate the properties of solid and liquid $^{4}\mathrm{He}$. The wave function is translationally invariant and symmetric under particle interchange. In principle, the calculations for the crystalline phase do not require the use of any auxiliary lattice. Using the Metropolis Monte Carlo algorithm, we show that the additional variational degrees of freedom in the wave function lower the energy significantly. This wave function also allows the crystalization of an equilibrated liquid phase when a crystalline seed is used. The pair correlation function and structure factor S(k) are determined in the liquid phase. The condensate fraction is calculated as well. Results are given for the single-particle distribution function around the lattice positions in the solid phase.

Scaling theory of the fractional quantum Hall effect.

A new class of variational wave functions is proposed for the fractional quantum Hall effect in the presence of disorder at arbitrary electron densities. A consequence of these wave functions is a law of corresponding states which relates the behavior of the system in the fractional Hall regime to that in the integer Hall regime. For example, it is shown that the transition from the 1/3 to 2/5 plateau should be characterized by the same critical exponents as the transition between integer plateaus, while the transition between the 1 and 4/3 plateaus may be first order, and thus have no critical behavior.

Class of variational singlet wave functions for the Hubbard model away from half filling.

We present a class of variational wave functions for strong-coupling Heisenberg Hubbard models. These are written in the form of three factors---a pair of determinants and a Jastrow function---and are made out of orbitals, {ital a} {ital la} Hartree-Fock theory, which solve a fictitious one-body problem. The wave functions respect various constraints known from general principles and appear to be potentially useful in understanding the possible behavior of the models in quantitative terms.

Singlet wave functions for the t-J model.

We investigate T=0 properties of the commensurate flux phases, a class of variational wave functions for the t-J model proposed recently by Anderson, Shastry, and Hristopoulos and which generalize the (1/2-flux state of Affleck and Marston away from half-filling. These states can be formally written in the quantum spin liquid form, the singlet bond amplitudes of which break the lattice translational symmetry. The supercell of the electromagnetic gauge (defining the fictitious flux) imposes the actual periodicities of the correlated wave function. Their order of commensurability with the lattice unit length is closely related to the hole density.

Anomalous quantum Hall effect and two-dimensional classical plasmas: Analytic approximations for correlation functions and ground-state energies

A simple analytic scheme is presented for the estimation of the two-point correlation function and the ground-state energy of a class of variational wave functions of interest in the study of the anomalous quantum Hall effect. The technique is illustrated by application to the wave function recently proposed by Laughlin and to a generalization of this wave function discussed by Halperin. The technique also yields information about the classical two-dimensional plasma problems associated with these wave functions.