Hamiltonian Lattice QED$_3$ with One and Two Flavors of Wilson Fermions: Topological Structure and Response

• URL: http://arxiv.org/abs/2603.05616v1
• Date: Thu, 05 Mar 2026 19:18:46 GMT
• Title: Hamiltonian Lattice QED$_3$ with One and Two Flavors of Wilson Fermions: Topological Structure and Response
• Abstract summary: We show that staggered-fermion discretizations in Hamiltonian gauge theories possesses an exact time-reversal symmetry.<n>In this work, we analyze fermion discretization effects in (2+1)D lattice Hamiltonians of fermions coupled to U(1) gauge fields that satisfy Gauss' law.
• Score: 5.803135196608668
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum simulation of topological phases in (2+1)D quantum electrodynamics with Wilson fermions provides a promising route toward realizing topological phenomena in near-term lattice experiments. We show that the commonly used staggered-fermion discretizations in Hamiltonian gauge theories possesses an exact time-reversal symmetry, which forbids the emergence of nontrivial topological phases and has led to confusion in the existing literature. In this work, we resolve this obstacle by systematically analyzing fermion discretization effects in (2+1)D lattice Hamiltonians of fermions coupled to U(1) gauge fields that satisfy Gauss' law. We show that Wilson fermions, already in the minimal one-flavor theory, naturally enable topological regimes with nonzero Chern numbers, and that the two-flavor extension at finite chemical potential further enriches the accessible topological structure. We develop gauge-invariant diagnostics of topological response, including many-body Chern numbers and current correlators that remain robust probes at weak coupling. Finally, through extensive exact diagonalization calculations across both flavor settings, we characterize the spectrum, correlators, and topological invariants, providing a concrete foundation for near-term quantum simulations of topological phases in lattice field theories. The implications of this work for quantum simulations of lattice field theory are analyzed in a joint submission [1].

Related papers

• Quantum Cellular Automata from Kramers-Wannier Dualities and Modular Relations [0.0]
  We show that QCAs associated with gravitational topological responses arise in several related settings.<n>We derive new projective $mathrmSL (2,mathbbZ_N)$ relations whose projective phases are gravitational topological responses constructed from Stiefel-Whitney classes.
  arXiv  Detail & Related papers  (2026-07-23T18:24:51Z)
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation [39.146761527401424]
  We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model.<n>We find a sequence of inhomogeneous ground states that arise through a real-space version of the mechanism of Hilbert-space fragmentation.
  arXiv  Detail & Related papers  (2025-06-23T14:19:35Z)
• A Path to Quantum Simulations of Topological Phases: (2+1)D Wilson Fermions Coupled To U(1) Background Gauge Fields [5.803135196608668]
  A key challenge in lattice formulations is the proper realization of topological phases and the Chern-Simons terms.<n>We analyze staggered and Wilson fermions coupled to $textU(1)$ background gauge fields in the Hamiltonian formulation.<n>Our findings resolve existing ambiguities in Hamiltonian formulations and provide a theoretical foundation for future quantum simulations of gauge theories with topological phases.
  arXiv  Detail & Related papers  (2025-04-30T17:33:01Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue [68.8204255655161]
  We study the phenomenon of cosmological particle production of Dirac fermions in a Friedman-Robertson-Walker spacetime. We present a scheme for the quantum simulation of this gravitational analogue by means of ultra-cold atoms in Raman optical lattices.
  arXiv  Detail & Related papers  (2022-12-02T18:28:23Z)
• Electric-magnetic duality and $\mathbb{Z}_2$ symmetry enriched Abelian lattice gauge theory [2.206623168926072]
  Kitaev's quantum double model is a lattice gauge theoretic realization of Dijkgraaf-Witten topological quantum field theory (TQFT) Topologically protected ground state space has broad applications for topological quantum computation and topological quantum memory.
  arXiv  Detail & Related papers  (2022-01-28T14:13:38Z)
• Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice [52.77024349608834]
  We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and non-local terms gives rise to a phase diagram with liquid phases with dominant cluster, spin, and density-wave quasi-long-range ordering.
  arXiv  Detail & Related papers  (2021-12-20T09:46:08Z)
• Entanglement Spectroscopy and probing the Li-Haldane Conjecture in Topological Quantum Matter [0.0]
  Topological phases are characterized by their entanglement properties. We propose to leverage the power of synthetic quantum systems for measuring entanglement via the Entanglement Hamiltonian.
  arXiv  Detail & Related papers  (2021-10-08T06:13:51Z)
• Conformal field theory from lattice fermions [77.34726150561087]
  We provide a rigorous lattice approximation of conformal field theories given in terms of lattice fermions in 1+1-dimensions. We show how these results lead to explicit error estimates pertaining to the quantum simulation of conformal field theories.
  arXiv  Detail & Related papers  (2021-07-29T08:54:07Z)
• Investigating a (3+1)D Topological $\theta$-Term in the Hamiltonian Formulation of Lattice Gauge Theories for Quantum and Classical Simulations [0.0]
  We derive the (3+1)D topological $theta$-term for Abelian and non-Abelian lattice gauge theories. We study numerically the zero-temperature phase structure of a (3+1)D U(1) lattice gauge theory.
  arXiv  Detail & Related papers  (2021-05-13T01:10:42Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit [58.720142291102135]
  Quasi-periodically driven quantum systems are predicted to exhibit quantized topological properties. We experimentally study a synthetic quantum Hall effect with a two-tone drive.
  arXiv  Detail & Related papers  (2020-04-07T15:00:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.