A Method for Studying Model Hamiltonians

S. A. Fedotov, M. B. Shirshov

Eli Chertkov, Bryan K. Clark

Traditional computational methods for studying quantum many-body systems are "forward methods," which take quantum models, i.e., Hamiltonians, as input and produce ground states as output.However, such forward methods often limit one's perspective to a small fraction of the space of possible Hamiltonians.We introduce an alternative computational "inverse method," the eigenstate-to-Hamiltonian construction (EHC), that allows us to better understand the vast space of quantum models describing strongly correlated systems.EHC takes as input a wave function jψ T i and produces as output Hamiltonians for which jψ T i is an eigenstate.This is accomplished by computing the quantum covariance matrix, a quantum mechanical generalization of a classical covariance matrix.EHC is widely applicable to a number of models and, in this work, we consider seven different examples.Using the EHC method, we construct a parent Hamiltonian with a new type of antiferromagnetic ground state, a parent Hamiltonian with two different targeted degenerate ground states, and large classes of parent Hamiltonians with the same ground states as well-known quantum models, such as the Majumdar-Ghosh model, the XX chain, the Heisenberg chain, the Kitaev chain, and a 2D BdG model.EHC gives an alternative inverse approach for studying quantum many-body phenomena.

N. N. Bogolyubov

A Method for Studying Model Hamiltonians: A Minimax Principle for Problems in Statistical Physics centers on methods for solving certain problems in statistical physics which contain four-fermion interaction. Organized into four chapters, this book begins with a presentation of the proof of the asymptotic relations for the many-time correlation functions. Chapter 2 details the construction of a proof of the generalized asymptotic relations for the many-time correlation averages. Chapter 3 explains the correlation functions for systems with four-fermion negative interaction. The last chapter sh

A. M. Kurbatov, S. S. Lapushkin

Yuan Liu, Minsik Cho, Brenda M. Rubenstein

We present an ab initio auxiliary field quantum Monte Carlo method for studying the electronic structure of molecules, solids, and model Hamiltonians at finite temperature. The algorithm marries the ab initio phaseless auxiliary field quantum Monte Carlo algorithm known to produce high accuracy ground state energies of molecules and solids with its finite temperature variant, long used by condensed matter physicists for studying model Hamiltonian phase diagrams, to yield a phaseless, ab initio finite temperature method. We demonstrate that the method produces internal energies within chemical accuracy of exact diagonalization results across a wide range of temperatures for H 2 O (STO-3G), C 2 (STO-6G), the one-dimensional hydrogen chain (STO-6G), and the multiorbital Hubbard model. Our method effectively controls the phase problem through importance sampling, often even without invoking the phaseless approximation, down to temperatures at which the systems studied approach their ground states and may therefore be viewed as exact over wide temperature ranges. This technique embodies a versatile tool for studying the finite temperature phase diagrams of a plethora of systems whose properties cannot be captured by a Hubbard U term alone. Our results moreover illustrate that the severity of the phase problem for model Hamiltonians far exceeds that for many molecules at all of the temperatures studied.