Related papers: Lefschetz Thimble Quantum Monte Carlo for Spin Sys…
The path optimization method, which is proposed to control the sign problem in quantum field theories with continuous degrees of freedom by machine learning, is applied to a spin model with discrete degrees of freedom. The path optimization…
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…
We present a numerically exact Inchworm Monte Carlo method for equilibrium multiorbital quantum impurity problems with general interactions and hybridizations. We show that the method, originally developed to overcome the dynamical sign…
We present novel Monte Carlo methods for treating the interacting shell model that allow exact calculations much larger than those heretofore possible. The two-body interaction is linearized by an auxiliary field; Monte Carlo evaluation of…
This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as…
The absence of negative sign problem in quantum Monte Carlo simulations of spin and fermion systems has different origins. World-line based algorithms for spins require positivity of matrix elements whereas auxiliary field approaches for…
We solve numerically exactly a simple toy model to quantum general relativity or more properly to path integral on a curved space. We consider the thermal equilibrium of a quantum many body problem on the sphere, the surface of constant…
The tempered Lefschetz thimble method (TLTM) is a parallel-tempering algorithm towards solving the numerical sign problem, where the system is tempered by the antiholomorphic gradient flow to tame both the sign and ergodicity problems…
We discuss two problems in complexified auxiliary fields in fermionic effective models, the auxiliary sign problem associated with the repulsive vector-field and the choice of the cut for the scalar field appearing from the logarithmic…
Quantum Monte Carlo method is applied to fractional quantum Hall systems. The use of the linear programming method enables us to avoid the negative-sign problem in the Quantum Monte Carlo calculations. The formulation of this method and the…
Building on recent solutions of the fermion sign problem for specific models we present two continuous-time quantum Monte Carlo methods for efficient simulation of mass-imbalanced Hubbard models on bipartite lattices at half-filling. For…
Path integrals with complex actions are encountered for many physical systems ranging from spin- or mass-imbalanced atomic gases and graphene to quantum chromo-dynamics at finite density to the non-equilibrium evolution of quantum systems.…
Monte Carlo methods play a central role in particle physics, where they are indispensable for simulating scattering processes, modeling detector responses, and performing multi-dimensional integrals. However, traditional Monte Carlo methods…
The Lefschetz thimble method, i.e., the integration along the steepest descent cycles, is an idea to evade the sign problem by complexifying the theory. We discuss that such steepest descent cycles can be identified as ground-state…
We investigate the inclusion of variable spins in electronic structure quantum Monte Carlo, with a focus on diffusion Monte Carlo with Hamiltonians that include spin-orbit interactions. Following our previous introduction of fixed-phase…
We consider the sign problem for classical spin models at complex $\beta =1/g_0^2$ on $L\times L$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$\beta$ than the reweighting Monte…
We study several aspects of the recently introduced fixed-phase spin-orbit diffusion Monte Carlo (FPSODMC) method, in particular, its relation to the fixed-node method and its potential use as a general approach for electronic structure…
Quantum Monte Carlo (QMC) methods are one of the most important tools for studying interacting quantum many-body systems. The vast majority of QMC calculations in interacting fermion systems require a constraint to control the sign problem.…
We present detailed discussions on a new approach we proposed in a previous paper to numerically study quantum spin systems. This method, which we will call re-structuring method hereafter, is based on rearrangement of intermediate states…
We follow up the work, where in light of the Picard-Lefschetz thimble approach, we split up the real-time path integral into two parts: the initial density matrix part which can be represented via an ensemble of initial conditions, and the…