Discrete Abelian lattice gauge theories on a ladder and their dualities
with quantum clock models
- URL: http://arxiv.org/abs/2208.04182v4
- Date: Mon, 12 Feb 2024 00:05:12 GMT
- Title: Discrete Abelian lattice gauge theories on a ladder and their dualities
with quantum clock models
- Authors: Sunny Pradhan, Andrea Maroncelli, Elisa Ercolessi
- Abstract summary: We study a duality transformation from the gauge-invariant subspace of a $mathbbZ_N$ lattice gauge theory to an $N$-clock model on a single chain.
The main feature of this mapping is the emergence of a longitudinal field in the clock model, whose value depends on the superselection sector of the gauge model.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We study a duality transformation from the gauge-invariant subspace of a
$\mathbb{Z}_N$ lattice gauge theory on a two-leg ladder geometry to an
$N$-clock model on a single chain. The main feature of this mapping is the
emergence of a longitudinal field in the clock model, whose value depends on
the superselection sector of the gauge model, implying that the different
sectors of the gauge theory can show quite different phase diagrams. In order
to investigate this and see if confined phases might emerge, we perform a
numerical analysis for $N = 2, 3, 4$, using exact diagonalization and DMRG.
Related papers
- Percolation renormalization group analysis of confinement in $\mathbb{Z}_2$ lattice gauge theories [0.0]
We develop a real-space renormalization group formalism for $mathbbZ$ LGTs using percolation probability as a confinement order parameter.
Our scheme enables future analytical studies of $mathZ$ LGTs with matter and quantum fluctuations and beyond.
arXiv Detail & Related papers (2024-06-25T12:51:44Z) - Entanglement of Gauge Theories: from the Toric Code to the
$\mathbb{Z}_2$ Lattice Gauge Higgs Model [2.570568710751949]
We show that mapping the toric code (TC) model to the Higgs ($mathbbZ$ GH) model has a non-trivial effect on the entanglement structure.
We derive a quantum channel that allows us to obtain the reduced density matrix of the $mathbbZ$ GH model from the one of the TC model.
arXiv Detail & Related papers (2023-11-27T19:00:02Z) - General quantum algorithms for Hamiltonian simulation with applications
to a non-Abelian lattice gauge theory [44.99833362998488]
We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers.
The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions.
The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
arXiv Detail & Related papers (2022-12-28T18:56:25Z) - New insights on the quantum-classical division in light of Collapse
Models [63.942632088208505]
We argue that the division between quantum and classical behaviors is analogous to the division of thermodynamic phases.
A specific relationship between the collapse parameter $(lambda)$ and the collapse length scale ($r_C$) plays the role of the coexistence curve in usual thermodynamic phase diagrams.
arXiv Detail & Related papers (2022-10-19T14:51:21Z) - A critical lattice model for a Haagerup conformal field theory [0.0]
We use the formalism of strange correlators to construct a critical classical lattice model in two dimensions.
We present compelling numerical evidence in the form of finite entanglement scaling to support a Haagerup conformal field theory.
arXiv Detail & Related papers (2021-10-07T14:57:52Z) - Boundary theories of critical matchgate tensor networks [59.433172590351234]
Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices.
For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states.
We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model.
arXiv Detail & Related papers (2021-10-06T18:00:03Z) - Rectification induced by geometry in two-dimensional quantum spin
lattices [58.720142291102135]
We address the role of geometrical asymmetry in the occurrence of spin rectification in two-dimensional quantum spin chains.
We show that geometrical asymmetry, along with inhomogeneous magnetic fields, can induce spin current rectification even in the XX model.
arXiv Detail & Related papers (2020-12-02T18:10:02Z) - Prediction of Toric Code Topological Order from Rydberg Blockade [0.0]
We find a topological quantum liquid (TQL) as evidenced by multiple measures.
We show how these can be measured experimentally using a dynamic protocol.
We discuss the implications for exploring fault-tolerant quantum memories.
arXiv Detail & Related papers (2020-11-24T19:00:05Z) - $\mathbb{Z}_N$ lattice gauge theory in a ladder geometry [0.0]
Hamiltonian lattice gauge theories defined in two-leg ladders.
We consider a model that includes both gauge boson and Higgs matter degrees of freedom with local $mathbbZ_N$ gauge symmetries.
arXiv Detail & Related papers (2020-11-12T17:48:25Z) - The Geometry of Time in Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
We continue the study of nonrelativistic quantum gravity associated with a family of Ricci flow equations.
This topological gravity is of the cohomological type, and it exhibits an $cal N=2$ extended BRST symmetry.
We demonstrate a standard one-step BRST gauge-fixing of a theory whose fields are $g_ij$, $ni$ and $n$, and whose gauge symmetries consist of (i) the topological deformations of $g_ij$, and (ii) the ultralocal nonrelativistic limit of space
arXiv Detail & Related papers (2020-11-12T06:57:10Z) - Tensor network models of AdS/qCFT [69.6561021616688]
We introduce the notion of a quasiperiodic conformal field theory (qCFT)
We show that qCFT can be best understood as belonging to a paradigm of discrete holography.
arXiv Detail & Related papers (2020-04-08T18:00:05Z)
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.