From Decay to Complete Breaking: Pulling the Strings in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>Yang-Mills Theory

Pepe, Michele; Wiese, U.‐J.

doi:10.1103/physrevlett.102.191601

Cited by 26 publications

(18 citation statements)

References 33 publications

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“…Nevertheless, a very important part of it, quantum chromodynamics (QCD), remains partially unresolved, due to its highly non-perturbative nature. One of the ways to tackle the non-perturbative physics of the strong interactions described by QCD is lattice gauge theories [1][2][3][4], which have been very successful in the study of a broad range of phenomena [5][6][7][8][9][10][11][12]. The most traditional methods of investigation of lattice gauge theories are based on Monte Carlo calculations in a Euclidean space-time and, in spite of their unquestionable efficiency to achieve many tasks, they present some limitations in specific cases.…”

Section: Introductionmentioning

confidence: 99%

Building projected entangled pair states with a local gauge symmetry

Zohar

Burrello

2016

New J. Phys.

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Tensor network states, and in particular projected entangled pair states (PEPS), suggest an innovative approach for the study of lattice gauge theories, both from a pure theoretic point of view, and as a tool for the analysis of the recent proposals for quantum simulations of lattice gauge theories. In this paper we present a framework for describing locally gauge invariant states on lattices using PEPS. The PEPS constructed hereby shall include both bosonic and fermionic states, suitable for all combinations of matter and gauge fields in lattice gauge theories defined by either finite or compact Lie groups.This last step has been undertaken for two-dimensional tensor networks in the recent works [46,48,55]. In particular, Tagliacozzo et al [46] introduced a formalism for building bosonic PEPS describing pure lattice gauge theories with arbitrary groups and adopted a truncation scheme for the representations which we will extend in this work to include matter and fermionic PEPS (fPEPS) as well; Haegeman et al [48] developed, instead, a general, conceptual formalism to build PEPS which describe both gauge fields and bosonic matter through a gauging map of injective PEPS. Finally, in [55], the authors presented an explicit analytical and numerical construction for the specific case of a truncated U(1) gauge-invariant state including both fermionic matter and bosonic gauge fields.In this work, we develop a more general framework for the construction of PEPS with local gauge invariance for lattice gauge theories whose gauge group G is either a compact Lie, or a finite group. We aim at unifying all the elements required for complete descriptions of lattice gauge theories: in particular we focus on gauge invariant states which include both matter and gauge fields and we propose a constructive approach to define tensor network states where the matter can be either bosonic or fermionic and is associated to an arbitrary representation of the gauge group. A special attention will indeed be devoted to the construction of fPEPS because of their more immediate relevance in the study of models which are closer to the usual particle physics theories.Throughout this paper we adopt the mathematical stucture discussed in [57] to describe the physical components of the PEPS and, in particular, the Hilbert spaces used to describe the matter and the gauge field degrees of freedom. We will show that such description, based on the representations of the gauge group, can be naturally extended to the virtual states constituting the links of the tensor network. Furthermore, to make this work self-contained, we will summarize the main elements of the construction presented in [57] without assuming that the reader is acquainted with PEPS or lattice gauge theories; the required PEPS details are reviewed and constructed along the paper, as well as their relations with lattice gauge theory.

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Section: Introductionmentioning

confidence: 99%

Building projected entangled pair states with a local gauge symmetry

Zohar

Burrello

2016

New J. Phys.

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“…Here we introduce a quantum simulator scheme to study the dynamics of an Abelian lattice gauge theory in which an initial electric field string can persist in time or break, in analogy with predictions of QCD [26][27][28]. We consider the Schwinger model with spinless fermions coupled to the electric field defined on links.…”

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confidence: 99%

Real-time-dynamics quantum simulation of (1+1)-dimensional lattice QED with Rydberg atoms

Notarnicola

Collura

Montangero

2020

Phys. Rev. Research

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We show how to implement a Rydberg-atom quantum simulator to study the non-equilibrium dynamics of an Abelian (1+1)-D lattice gauge theory. The implementation locally codifies the degrees of freedom of a Z3 gauge field, once the matter field is integrated out by means of the Gauss' local symmetries. The quantum simulator scheme is based on current available technology and scalable to considerable lattice sizes. It allows, within experimentally reachable regimes, to explore different string dynamics and to infer information about the Schwinger U (1) model.

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“…The above Hamiltonian resembles the Schwinger model [37]. For S = 1 it shares the nonperturbative phenomenon of string breaking by dynamical qq pair creation with QCD [38]. An external static quark-anti-quark pairQQ (with the Gauss law appropriately taken into account) is connected by a confining electric flux string (Fig.…”

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confidence: 99%