Related papers: Towards overcoming the Monte Carlo sign problem wi…
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour…
Quantum Monte Carlo simulations provide one of the more powerful and versatile numerical approaches to condensed matter systems. However, their application to frustrated quantum spin models, in all relevant temperature regimes, is hamstrung…
To tackle the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the original…
We use tensor network techniques to obtain high order perturbative diagrammatic expansions for the quantum many-body problem at very high precision. The approach is based on a tensor train parsimonious representation of the sum of all…
Tensor networks offer a sign-problem-free approach to study lattice gauge theories, but extracting precise universal information associated with the deconfinement transition remains challenging. In this work, we study the deconfinement…
We present a new approach for Monte Carlo simulations of lattice quantum spin systems which is able to eliminate the negative sign problem. Its complexity is linear in the volume of the lattice. Its efficiency is tested on a simple…
We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to…
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…
We consider the problem of tensor estimation from noisy observations with possibly missing entries. A nonparametric approach to tensor completion is developed based on a new model which we coin as sign representable tensors. The model…
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties, without the sign problem. The list spans condensed matter, nuclear physics, and…
Quantum Monte Carlo simulations of fermions are hampered by the notorious sign problem whose most striking manifestation is an exponential growth of sampling errors with the number of particles. With the sign problem known to be an NP-hard…
Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from highly oscillatory phase of the path integral. In this letter, we present a new method to compute real time quantities on the…
We study the sign problem in the Hubbard model on the hexagonal lattice away from half-filling using the Lefschetz thimbles method. We identify the saddle points, reduce their amount, and perform quantum Monte Carlo (QMC) simulations using…
This is a review of recent developments in Monte Carlo methods in the field of ultra cold gases. For bosonic atoms in an optical lattice we discuss path integral Monte Carlo simulations with worm updates and show the excellent agreement…
We present an exact Monte Carlo algorithm designed to sample theories where the energy is a sum of many couplings of decreasing strength. The algorithm avoids the computation of almost all non-leading terms. Its use is illustrated by…
The design and application of regression-free tensor network representations for integration is presented. Tensor network methods are demonstrated to outperform Monte Carlo for test problems, and exponential convergence is shown to be…
The tensor network algorithm, a family of prevalent numerical methods for quantum many-body problems, aptly captures the entanglement properties intrinsic to quantum systems, enabling precise representation of quantum states. However, its…
Tensor networks provide a natural language for non-invertible symmetries in general Hamiltonian lattice models. We use ZX-diagrams, which are tensor network presentations of quantum circuits, to define a non-invertible operator implementing…
We study a tensor network formulation of the two dimensional lattice $\mathcal{N}=1$ Wess-Zumino model with Wilson derivatives for both fermions and bosons. The tensor renormalization group allows us to compute the partition function…
Although numerical simulation in lattice field theory is one of the most effective tools to study non-perturbative properties of field theories, it faces serious obstacles coming from the sign problem in some theories such as finite density…