Simulating 2+1D Z_{3} Lattice Gauge Theory with an Infinite Projected Entangled-Pair State.

Daniel Robaina,J Ignacio Cirac,Mari Carmen Bañuls

doi:10.1103/physrevlett.126.050401

Abstract

We simulate a zero-temperature pure Z_{3} lattice gauge theory in 2+1 dimensions by using an iPEPS (infinite projected entangled-pair state) Ansatz for the ground state. Our results are therefore directly valid in the thermodynamic limit. They clearly show two distinct phases separated by a phase transition. We introduce an update strategy that enables plaquette terms and Gauss-law constraints to be applied as sequences of two-body operators. This allows the use of the most up-to-date iPEPS algorithms. From the calculation of spatial Wilson loops we are able to prove the existence of a confined phase. We show that with relatively low computational cost it is possible to reproduce crucial features of gauge theories. We expect that the strategy allows the extension of iPEPS studies to more general LGTs.

Highlights

Introduction.—For years, tensor networks (TN) have been exploited to study quantum many-body problems, especially in the context of condensed matter physics, since they provide efficient Ansätze for ground states, low lying excitations and thermal equilibrium states of local Hamiltonians [1,2,3,4,5]
The one-dimensional success strongly motivates an extension of the TN study to lattice gauge theories (LGT) in higher spatial dimensions, where the natural generalization of the matrix product state (MPS) Ansatz is provided by projected entangled pair states (PEPS) [8], or its infinite version defined directly in the thermodynamic limit, iPEPS [9]
The fast progress in iPEPS algorithms has allowed reaching some of the most competitive results for certain condensed matter problems [14,15,16,17,18,19,20] and there is no conceptual limitation to apply them to LGTs [21], until the date the only numerical results of (i) PEPS simulations of LGTs have been limited to very simple toy models, or did not perform an actual optimization of the most general tensors [22,23,24,25,26,27]

Summary

Introduction

Introduction.—For years, tensor networks (TN) have been exploited to study quantum many-body problems, especially in the context of condensed matter physics, since they provide efficient Ansätze for ground states, low lying excitations and thermal equilibrium states of local Hamiltonians [1,2,3,4,5]. We simulate a zero-temperature pure Z3 lattice gauge theory in 2 þ 1 dimensions by using an iPEPS (infinite projected entangled-pair state) Ansatz for the ground state.

Results

Conclusion