Building projected entangled pair states with a local gauge symmetry

Zohar, Erez; Burrello, Michele

doi:10.1088/1367-2630/18/4/043008

Cited by 52 publications

(69 citation statements)

References 70 publications

(153 reference statements)

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“…The analysis of real-time dynamics is also lacking, since Monte Carlo simulations only allow to calculate Euclidean space-time correlation functions in imaginary time (after a Wick rotation).In this context, two different approaches have been recently proposed to study lattice gauge theories in regimes that cannot be accessed using previous techniques. One involves the application of methods based on tensor networks [56][57][58][59][60][61][62][63][64][65][66][67][68][69]. Another consists on performing quantum simulations using low energy quantum systems.…”

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confidence: 99%

Quantum simulation of the Abelian-Higgs lattice gauge theory with ultracold atoms

2017

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We present a quantum simulation scheme for the Abelian-Higgs lattice gauge theory using ultracold bosonic atoms in optical lattices. The model contains both gauge and Higgs scalar fields, and exhibits interesting phases related to confinement and the Higgs mechanism. The model can be simulated by an atomic Hamiltonian, by first mapping the local gauge symmetry to an internal symmetry of the atomic system, the conservation of hyperfine angular momentum in atomic collisions. By including auxiliary bosons in the simulation, we show how the Abelian-Higgs Hamiltonian emerges effectively. We analyze the accuracy of our method in terms of different experimental parameters, as well as the effect of the finite number of bosons on the quantum simulator. Finally, we propose possible experiments for studying the ground state of the system in different regimes of the theory, and measuring interesting high energy physics phenomena in real time. allows us to obtain information about systems that cannot be accessed experimentally, by investigating others for which state preparation and measurements are much easier tasks.Among the relevant platforms that can serve as quantum simulators, both analog and digital, many atomic and optical systems stand out due to their remarkable experimental controllability. Some examples include ultracold atoms [5][6][7][8][9], trapped ions [10][11][12][13][14], photonic systems [15] and Rydberg atoms [16]. Ultracold atoms in optical lattices, in particular, present the possibility of recreating many different interactions-such as nearestneighbor, long-range forces, on-site interactions, etc-allowing for the simulation of both condensed matter and high energy physics models. Solid-state systems, such as quantum dots [17][18][19] or superconducting circuits [20,21], also show prominent results that make them interesting candidates to perform quantum simulations.Using these ideas, many condensed matter Hamiltonians have been considered for quantum simulations, some of them even realized experimentally. Some examples include spin systems [14,[22][23][24], such as the Ising or Heisenberg models; the Bose-Hubbard model [5,25]; the Tonks-Girardeau gas [26], or copper-oxide superconductors [18]. External gauge potentials can be simulated as well, allowing for the study of the fractional quantum Hall effect [27] and other topological phenomena [28-31]. Quantum simulations of high energy physics models, although more demanding than their condensed matter counterparts, are also possible. Some examples include the simulation of the Dirac [32-34] and Majorana equations [35], the Casimir force [36], the Schwinger mechanism [37] or the oscillations of neutrinos [38, 39]. Simulations of quantum field theories [40, 41], gravitational theories [42] and black holes [43, 44] have been proposed in recent years, some of them realized experimentally as well [45].Within high energy physics, gauge theories are particularly relevant, since they lie in the core of the Standard Model of particle physics [46][47][48][49]; dyn...

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confidence: 99%

Quantum simulation of the Abelian-Higgs lattice gauge theory with ultracold atoms

2017

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“…using PEPS. In our work we were able to connect some of the results to the symmetry properties and structure of previous gauge invariant PEPS constructions [31,32,34] when the space dimension is reduced to one, and therefore higher dimensional generalizations in the spirit of the current work should be possible. In particular, the tensor describing the gauge field, as it resides on the links of a lattice, is a one dimensional object for any spatial dimension, and has shown, in some particular cases, properties known from previous PEPS studies.…”

Section: Discussionmentioning

confidence: 80%

“…Example V.3 (An SU (2) gauge invariant MPV). For G = SU (2) we demonstrate the construction of a general locally invariant MPV emphasizing the constituents of physical theories and relating our setting and notation to [34,36]. Write the irreducible representations D j (g) in terms of their generators: D j (g) = exp i a τ j a ϕ a (g) , ∀g ∈ SU (2),…”

Section: Note That the Bond Dimension Of The Tensormentioning

confidence: 99%

Classification of matrix product states with a local (gauge) symmetry

et al. 2017

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Matrix Product States (MPS) are a particular type of one dimensional tensor network states, that have been applied to the study of numerous quantum many body problems. One of their key features is the possibility to describe and encode symmetries on the level of a single building block (tensor), and hence they provide a natural playground for the study of symmetric systems. In particular, recent works have proposed to use MPS (and higher dimensional tensor networks) for the study of systems with local symmetry that appear in the context of gauge theories. In this work we classify MPS which exhibit local invariance under arbitrary gauge groups. We study the respective tensors and their structure, revealing known constructions that follow known gauging procedures, as well as different, other types of possible gauge invariant states.

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“…In particular, we will exploit the formalism adopted for the quantum simulations of lattice gauge theories (see, for example, the reviews [16,17]) and we will adopt the notation developed in Refs. [18,19] for their tensor-network study.…”

Section: B the Rung Hilbert Space And Operatorsmentioning

confidence: 99%

Dyonic zero-energy modes

2018

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One-dimensional systems with topological order are intimately related to the appearance of zeroenergy modes localized on their boundaries. The most common example is the Kitaev chain, which displays Majorana zero-energy modes and it is characterized by a two-fold ground state degeneracy related to the global Z2 symmetry associated with fermionic parity. By extending the symmetry to the ZN group, it is possible to engineer systems hosting topological parafermionic modes. In this work, we address one-dimensional systems with a generic discrete symmetry group G. We define a ladder model of gauge fluxes that generalizes the Ising and Potts models and displays a symmetry broken phase. Through a non-Abelian Jordan-Wigner transformation, we map this flux ladder into a model of dyonic operators, defined by the group elements and irreducible representations of G. We show that the so-obtained dyonic model has topological order, with zero-energy modes localized at its boundary. These dyonic zero-energy modes are in general weak topological modes, but strong dyonic zero modes appear when suitable position-dependent couplings are considered. arXiv:1807.09286v2 [cond-mat.str-el]

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Building projected entangled pair states with a local gauge symmetry

Cited by 52 publications

References 70 publications

Quantum simulation of the Abelian-Higgs lattice gauge theory with ultracold atoms

Quantum simulation of the Abelian-Higgs lattice gauge theory with ultracold atoms

Classification of matrix product states with a local (gauge) symmetry

Dyonic zero-energy modes

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