Variational Equations-of-States for Interacting Quantum Hamiltonians
- URL: http://arxiv.org/abs/2307.00812v1
- Date: Mon, 3 Jul 2023 07:51:15 GMT
- Title: Variational Equations-of-States for Interacting Quantum Hamiltonians
- Authors: Wenxin Ding
- Abstract summary: We present variational equations of state (VES) for pure states of an interacting quantum Hamiltonian.
VES can be expressed in terms of the variation of the density operators or static correlation functions.
We present three nontrivial applications of the VES.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Variational methods are of fundamental importance and widely used in
theoretical physics, especially for strongly interacting systems. In this work,
we present a set of variational equations of state (VES) for pure states of an
interacting quantum Hamiltonian. The VES can be expressed in terms of the
variation of the density operators or static correlation functions. We derive
the algebraic relationship between a known pure state density matrix and its
variation, and obtain the VES by applying this relation to the averaged
Heisenberg-equations-of-motion for the exact density matrix. Additionally, we
provide a direct expression of the VES in terms of correlation functions to
make it computable. We present three nontrivial applications of the VES: a
perturbation calculation of correlation functions of the transverse field Ising
model in arbitrary spatial dimensions, a study of a longitudinal field
perturbation to the one-dimensional transverse field Ising model at the
critical point and variational calculation of magnetization and ground state
energy of the two-dimensional spin-1/2 Heisenberg model on a square lattice.
For the second one, our results not only recover the scaling limit, but also
indicate the possibility of continuous tuning of the critical exponents by
adjusting the longitudinal fields differently from the scaling limit. For the
Heisenberg model, we obtained results numerically comparable to established
results with simple calculations. The VES approach provides a powerful and
versatile tool for studying interacting quantum systems.
Related papers
- First-Order Phase Transition of the Schwinger Model with a Quantum Computer [0.0]
We explore the first-order phase transition in the lattice Schwinger model in the presence of a topological $theta$-term.
We show that the electric field density and particle number, observables which reveal the phase structure of the model, can be reliably obtained from the quantum hardware.
arXiv Detail & Related papers (2023-12-20T08:27:49Z) - Quench dynamics in higher-dimensional Holstein models: Insights from Truncated Wigner Approaches [41.94295877935867]
We study the melting of charge-density waves in a Holstein model after a sudden switch-on of the electronic hopping.
A comparison with exact data obtained for a Holstein chain shows that a semiclassical treatment of both the electrons and phonons is required in order to correctly describe the phononic dynamics.
arXiv Detail & Related papers (2023-12-19T16:14:01Z) - Variational manifolds for ground states and scarred dynamics of blockade-constrained spin models on two and three dimensional lattices [0.0]
We introduce a variational manifold of simple tensor network states for the study of a family of constrained models that describe spin-1/2 systems.
Our method can be interpreted as a generalization of mean-field theory to constrained spin models.
arXiv Detail & Related papers (2023-11-15T13:52:21Z) - Message-Passing Neural Quantum States for the Homogeneous Electron Gas [41.94295877935867]
We introduce a message-passing-neural-network-based wave function Ansatz to simulate extended, strongly interacting fermions in continuous space.
We demonstrate its accuracy by simulating the ground state of the homogeneous electron gas in three spatial dimensions.
arXiv Detail & Related papers (2023-05-12T04:12:04Z) - Quantum Simulation for Partial Differential Equations with Physical
Boundary or Interface Conditions [28.46014452281448]
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions.
We implement this method for several typical problems, including the linear convection equation with inflow boundary conditions and the heat equation with Dirichlet and Neumann boundary conditions.
For interface problems, we study the (parabolic) Stefan problem, linear convection, and linear Liouville equations with discontinuous and even measure-valued coefficients.
arXiv Detail & Related papers (2023-05-04T10:32:40Z) - Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solvers [32.57938108395521]
A class of mechanistic models, Linear partial differential equations, are used to describe physical processes such as heat transfer, electromagnetism, and wave propagation.
specialized numerical methods based on discretization are used to solve PDEs.
By ignoring parameter and measurement uncertainty, classical PDE solvers may fail to produce consistent estimates of their inherent approximation error.
arXiv Detail & Related papers (2022-12-23T17:02:59Z) - Alternative quantisation condition for wavepacket dynamics in a
hyperbolic double well [0.0]
We propose an analytical approach for computing the eigenspectrum and corresponding eigenstates of a hyperbolic double well potential of arbitrary height or width.
Considering initial wave packets of different widths and peak locations, we compute autocorrelation functions and quasiprobability distributions.
arXiv Detail & Related papers (2020-09-18T10:29:04Z) - Probing eigenstate thermalization in quantum simulators via
fluctuation-dissipation relations [77.34726150561087]
The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems.
Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations.
Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
arXiv Detail & Related papers (2020-07-20T18:00:02Z) - Efficient variational contraction of two-dimensional tensor networks
with a non-trivial unit cell [0.0]
tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems.
We generalize a recently proposed variational uniform matrix product state algorithm for capturing one-dimensional quantum lattices.
A key property of the algorithm is a computational effort that scales linearly rather than exponentially in the size of the unit cell.
arXiv Detail & Related papers (2020-03-02T19:01:06Z) - Variational-Correlations Approach to Quantum Many-body Problems [1.9336815376402714]
We investigate an approach for studying the ground state of a quantum many-body Hamiltonian.
The challenge set by the exponentially-large Hilbert space is circumvented by approximating the positivity of the density matrix.
We demonstrate the ability of this approach to produce long-range correlations, and a ground-state energy that converges to the exact result.
arXiv Detail & Related papers (2020-01-17T19:52:54Z) - Fast approximations in the homogeneous Ising model for use in scene
analysis [61.0951285821105]
We provide accurate approximations that make it possible to numerically calculate quantities needed in inference.
We show that our approximation formulae are scalable and unfazed by the size of the Markov Random Field.
The practical import of our approximation formulae is illustrated in performing Bayesian inference in a functional Magnetic Resonance Imaging activation detection experiment, and also in likelihood ratio testing for anisotropy in the spatial patterns of yearly increases in pistachio tree yields.
arXiv Detail & Related papers (2017-12-06T14:24:34Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.