Emergence of Gauss' Law in a $Z_2$ Lattice Gauge Theory

Frank, Jernej; Huffman, Emilie; Chandrasekharan, Shailesh

doi:10.48550/arxiv.1904.05414

Cited by 3 publications

(3 citation statements)

References 26 publications

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“…Exactly solvable models of a nonstandard Z 2 gauge theory coupled to fermionic matter were constructed [12] and argued to exhibit disorder-free localization [13]. Fermions at finite density coupled to Ising gauge theory without the Gauss law were studied in [14,15]. For related recent work on unconstrained Z 2 gauge theories coupled to bosonic matter, see [16].…”

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confidence: 99%

Confined Phases of One-Dimensional Spinless Fermions Coupled to Z2 Gauge Theory

et al. 2020

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We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical Z2 gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the Density Matrix Renormalization Group the system is shown to form a Luttinger liquid, indicating the emergence of fractionalized excitations despite the confinement of lattice fermions. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system. We discuss the possibility of a Mott phase at the commensurate filling 2/3.

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confidence: 99%

Confined Phases of One-Dimensional Spinless Fermions Coupled to Z2 Gauge Theory

et al. 2020

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“…Model.-Here, we focus on out-of-equilibrium dynamics, which is highly pertinent for current quantum simulators in ultracold atomic gases [14,[16][17][18] and for which emergent gauge symmetry has received considerably less attention. Although our discussion is general, for concreteness, we consider a Z 2 gauge theory [33][34][35][36] coupled to matter inspired by a recent experiment [16] we mostly consign similar results for a U(1) gauge theory to the SM [37].…”

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confidence: 99%

Reliability of Lattice Gauge Theories

Halimeh

Hauke

2020

Phys. Rev. Lett.

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Currently, there are intense experimental efforts to realize lattice gauge theories in quantum simulators. Except for specific models, however, practical quantum simulators can never be fine-tuned to perfect local gauge invariance. There is thus a strong need for a rigorous understanding of gauge-invariance violation and how to reliably protect against it. As we show through analytic and numerical evidence, in the presence of a gauge invariance-breaking term the gauge violation accumulates only perturbatively at short times before proliferating only at very long times. This proliferation can be suppressed up to infinite times by energetically penalizing processes that drive the dynamics away from the initial gauge-invariant sector. Our results provide a theoretical basis that highlights a surprising robustness of gauge-theory quantum simulators.

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“…Anticipating this possibility, the field has exploded in recent years with new ideas and algorithms for using quantum computers to understand quantum many body systems and quantum field theories [4][5][6][7][8][9][10][11]. Simple one dimensional quantum field theories are currently being studied extensively [12][13][14][15][16][17][18].…”

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confidence: 99%

Qubit regularization of theO(3)sigma model

Singh

Chandrasekharan

2019

Phys. Rev. D

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We construct a qubit regularization of the O(3) non-linear sigma model in two and three spatial dimensions using a quantum Hamiltonian with two qubits per lattice site. Using a worldline formulation and worm algorithms, we show that in two spatial dimensions our model has a quantum critical point where the well-known scale-invariant physics of the three-dimensional Wilson-Fisher fixed point is reproduced. In three spatial dimensions, we recover mean-field critical exponents at a similar quantum critical point. These results show that our qubit Hamiltonian is in the same universality class as the traditional classical lattice model close to the critical points. Simple modifications to our model also allow us to study the physics of traditional lattice models with O(2) and Z2 symmetries close to the corresponding critical points.

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Emergence of Gauss' Law in a $Z_2$ Lattice Gauge Theory

Cited by 3 publications

References 26 publications

Confined Phases of One-Dimensional Spinless Fermions Coupled to Z2 Gauge Theory

Confined Phases of One-Dimensional Spinless Fermions Coupled to Z2 Gauge Theory

Reliability of Lattice Gauge Theories

Qubit regularization of theO(3)sigma model

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