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We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…
Quantum Monte Carlo simulations of quantum many body systems are plagued by the Fermion sign problem. The computational complexity of simulating Fermions scales exponentially in the projection time $\beta$ and system size. The sign problem…
The unitarity limit describes interacting particles where the range of the interaction is zero and the scattering length is infinite. We present precision benchmark calculations for two-component fermions at unitarity using three different…
Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian circumvents this problem. We show that the modified…
We study a Hamiltonian lattice version of the two-dimensional Wess-Zumino model. Preliminary results obtained by Quantum Monte Carlo with a many-parameter guiding wave function are presented. We analyze the pattern of supersymmetry breaking…
In this paper, we present details of the dual fermion (DF) method to study the non-local correction to single site DMFT. The DMFT two-particle Green's function is calculated using continuous time quantum monte carlo (CT-QMC) method. The…
A 'forward walking' Green's Function Monte Carlo algorithm is used to obtain expectation values for SU(3) lattice Yang-Mills theory in (3+1) dimensions. The ground state energy and Wilson loops are calculated, and the finite-size scaling…
The entanglement entropy probing novel phases and phase transitions numerically via quantum Monte Carlo has made great achievements in large-scale interacting spin/boson systems. In contrast, the numerical exploration in interacting fermion…
We introduce a novel method within the shell model Monte Carlo approach to calculate the ground-state energy of a finite-size system with an odd number of particles by using the asymptotic behavior of the imaginary-time single-particle…
We present a practical analysis of the fermion sign problem in fermionic path integral Monte Carlo (PIMC) simulations in the grand-canonical ensemble (GCE). As a representative model system, we consider electrons in a $2D$ harmonic trap. We…
We propose a new Monte Carlo algorithm for the numerical study of general lattice models in Hamiltonian form. The algorithm is based on an initial Ansatz for the ground state wave function depending on a set of free parameters which are…
Monte Carlo simulations are a powerful tool for elucidating the properties of complex systems across many disciplines. Not requiring any a priori knowledge, they are particularly well suited for exploring new phenomena. However, when…
The Holstein model of spinless fermions interacting with dispersionless phonons in one dimension is studied by a Green's function Monte Carlo technique. The ground state energy, first fermionic excited state, density wave correlations, and…
Diagrammatic Monte Carlo approach is applied to a problem of a single spin-down fermion resonantly interacting with the sea of ideal spin-up fermions. On one hand, we develop a generic, sign-problem tolerant, method of exact numerical…
The conventional second-order Path Integral Monte Carlo method is plagued with the sign problem in solving many-fermion systems. This is due to the large number of anti-symmetric free fermion propagators that are needed to extract the…
Monte Carlo is one of the most useful methods to study the quantum Hall problems. In this paper, we introduce a fast lattice Monte Carlo method based on a mathematically exact reformulation of the torus quantum Hall problems from continuum…
Ground state properties of the Hubbard model are of fundamental importance to understand the mechanism of unconventional superconductivity in the high-T_c cuprates and other materials. One of the most powerful numerical methods for strongly…
A ``forward walking'' Quantum Monte Carlo (QMC) algorithm has been developed to calculate correlation functions for the Hamiltonian lattice formulation of U(1) Yang-Mills theory in (2+1) dimensions. It is shown that Wilson loops can be…
We propose a framework based on the concept of the semigroup to understand the fermion sign problem. By using properties of contraction semigroups, we obtain sufficient conditions for quantum lattice fermion models to be sign-problem-free.…
The `dynamic' Hubbard Hamiltonian describes interacting fermions on a lattice whose on-site repulsion is modulated by a coupling to a fluctuating bosonic field. We investigate one such model, introduced by Hirsch, using the determinant…