Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2012.08543 · Physical review. B./Physical review. B

Quantum phases of two-dimensional Z2 gauge theory coupled to single-component fermion matter

Umberto Borla, Bhilahari Jeevanesan, Frank Pollmann, Sergej Moroz

Published Feb 16, 2022• 26 citations
arXivHTMLPDF

Abstract

Gauge theories are ubiquitous in contemporary physics. Here, the authors investigate the many-body phase diagram of a model where dynamical discrete Ising gauge fields mediate interactions between single-component fermionic matter. Such a system remained intractable for years, due to the lack of sign-problem-free Monte-Carlo simulations. With the help of a combination of analytical and state-of-the-art numerical tensor-network-based methods, the authors uncover the salient features of an intricate quantum phase diagram and reveal surprising aspects of quantum constrained dynamics. The recent advances in cold-atoms-based setups might soon allow experimental explorations of this model.

DOI
10.1103/physrevb.105.075132

Related papers

Deconfined quantum criticality in Ising gauge theory entangled with single-component fermions

Umberto Borla, Snir Gazit, Sergej Moroz

Investigating novel manifestations of quantum criticality is central to modern theoretical condensed matter physics. Here, the authors unveil the exotic quantum phase diagram of a two-dimensional system of single-component fermions, minimally coupled to dynamical Ising gauge fields. With state-of-the-art numerical methods, the authors detect a robust quantum critical line, where gauge confinement and translation symmetry breaking occur simultaneously. The authors conjecture a $u(1)$ deconfined criticality scenario, and propose a corresponding low-energy effective field theory of the exotic quantum critical point.

arXiv:2402.00933•Physical review. B./Physical review. B•Nov 19, 2024•2 citations

Quantum phases of two-dimensional $\mathbb{Z}_2$ gauge theory coupled to spinless fermion matter

Umberto Borla, Bhilahari Jeevanesan, Frank Pollmann +1 more

We investigate the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with $U(1)$ symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model reduces to (i) pure $\mathbb{Z}_2$ even and odd gauge theories, (ii) free fermions in a static background of deconfined $\mathbb{Z}_2$ gauge fields, (iii) the kinetic Rokhsar-Kivelson quantum dimer model at a generic dimer filling. We develop a local transformation that maps the lattice gauge theory onto a model of $\mathbb{Z}_2$ gauge-invariant spin $1/2$ degrees of freedom. Using the mapping, we perform numerical density matrix renormalization group calculations that corroborate our understanding of the limits identified above. Moreover, in the absence of the magnetic plaquette term, we reveal signatures of topologically ordered Dirac semimetal and staggered Mott insulator phases at half-filling. At strong coupling, the lattice gauge theory displays fracton phenomenology with isolated fermions being completely frozen and dimers exhibiting restricted mobility. In that limit, we predict that in the ground state dimers form compact clusters, whose hopping is suppressed exponentially in their size. We determine the band structure of the smallest clusters numerically using exact diagonalization.

•Dec 17, 2020•0 citations

Constrained many-body phases in a $\mathbb{Z}_2$-Higgs lattice gauge theory

Alexander Schuckert, Stefan Kühn, Smith, Kevin C. +2 more

We study the ground-state phase diagram of a one-dimensional $\mathbb{Z}_2$ lattice gauge theory coupled to soft-core bosonic matter at unit filling, inspired by the Higgs sector of the standard model. Through a combination of analytical perturbative approaches, exact diagonalization, and density-matrix-renormalization-group simulations, we uncover a rich phase diagram driven by gauge-field-mediated resonant pair hopping and the confinement of single particles. The pair hopping results in a bunching state with superextensive energy and macroscopic particle number fluctuations at strong electric field strengths and weak on-site interactions. The bunching state crosses over into a pair superfluid phase as the on-site interaction increases, characterized by a finite superfluid density and powerlaw-decaying pair correlations. At large on-site interaction strengths and driven by effective interactions induced by the gauge constraint, the superfluid transitions into an incompressible pair Mott insulator phase. At weak field strengths and on-site interactions, we find a plasma-like region, where single bosons exhibit large short-range correlations and the ground state is composed almost equally of states with even and odd local boson occupation. The presence of a bunching state with large number fluctuations, which is difficult to study using classical numerics, motivates experimental realizations in hybrid boson-qubit quantum simulation platforms such as circuit QED, neutral atoms, and trapped ions. Our findings highlight the rich interplay between gauge fields and soft-core bosonic matter.

arXiv:2503.03828•Mar 5, 2025•0 citations

Fractionalized holes in one-dimensional Z2 gauge theory coupled to fermion matter: Deconfined dynamics and emergent integrability

Aritra Das, Umberto Borla, Sergej Moroz

We investigate the interplay of quantum one-dimensional discrete ${\mathbb{Z}}_{2}$ gauge fields and fermion matter near full filling in terms of deconfined fractionalized hole excitations that constitute mobile domain walls between vacua that break spontaneously translation symmetry. In the limit of strong string tension, we uncover emergent integrable correlated hopping dynamics of holes which is complementary to the constrained XXZ description in terms of bosonic dimers. We analyze numerically quantum dynamics of spreading of an isolated hole together with the associated time evolution of entanglement and provide analytical understanding of its salient features. We also study the model enriched with a short-range interaction and clarify the nature of the resulting ground state at low filling of holes and identify deconfined hole excitations near the hole filling ${\ensuremath{\nu}}^{h}=1/3$.

arXiv:2111.13205•Physical review. B./Physical review. B•Feb 16, 2023•5 citations

Lattice quantum electrodynamics in (3+1)-dimensions at finite density with tensor networks

Giuseppe Magnifico, Timo Felser, Pietro Silvi +1 more

Gauge theories are of paramount importance in our understanding of fundamental constituents of matter and their interactions. However, the complete characterization of their phase diagrams and the full understanding of non-perturbative effects are still debated, especially at finite charge density, mostly due to the sign-problem affecting Monte Carlo numerical simulations. Here, we report the Tensor Network simulation of a three dimensional lattice gauge theory in the Hamiltonian formulation including dynamical matter: Using this sign-problem-free method, we simulate the ground states of a compact Quantum Electrodynamics at zero and finite charge densities, and address fundamental questions such as the characterization of collective phases of the model, the presence of a confining phase at large gauge coupling, and the study of charge-screening effects.

arXiv:2011.10658•Nature Communications•Jun 14, 2021•80 citations

Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases

Xiao Yan Xu, Yang Qi, Long Zhang +3 more

The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics.However, except for certain limits (for instance, a large number of flavors of matter fields), analytical methods can provide few concrete results.Here we show that the problem of compact Uð1Þ lattice gauge theory coupled to fermionic matter in ð2 þ 1ÞD is possible to access via sign-problem-free quantum Monte Carlo simulations.One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations.By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous-symmetrybreaking phases such as the valence-bond solid (VBS) and Néel antiferromagnet emerge.Deconfined phases with algebraic spin and VBS correlation functions are also observed.Such deconfined phases are incarnations of exotic states of matter, i.e., the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases.The phase transitions between the deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality.In particular, for four flavors N f ¼ 4, our data suggest a continuous quantum phase transition between the VBS and Néel order.We also provide preliminary theoretical analysis for these quantum phase transitions.

arXiv:1807.07574•Physical Review X•May 2, 2019•98 citations
Gauge theories are ubiquitous in contemporary physics. Here, the authors investigate the many-body phase diagram of a model where dynamical discrete Ising gauge fields mediate interactions between single-component fermionic matter. Such a system remained intractable for years, due to the lack of sign-problem-free Monte-Carlo simulations. With the help of a combination of analytical and state-of-the-art numerical tensor-network-based methods, the authors uncover the salient features of an intricate quantum phase diagram and reveal surprising aspects of quantum constrained dynamics. The recent advances in cold-atoms-based setups might soon allow experimental explorations of this model.
Investigating novel manifestations of quantum criticality is central to modern theoretical condensed matter physics. Here, the authors unveil the exotic quantum phase diagram of a two-dimensional system of single-component fermions, minimally coupled to dynamical Ising gauge fields. With state-of-the-art numerical methods, the authors detect a robust quantum critical line, where gauge confinement and translation symmetry breaking occur simultaneously. The authors conjecture a u(1)u(1)u(1) deconfined criticality scenario, and propose a corresponding low-energy effective field theory of the exotic quantum critical point.
Quantum phases of two-dimensional Z2\mathbb{Z}_2Z2​ gauge theory coupled to spinless fermion matter
We investigate the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with U(1)U(1)U(1) symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model reduces to (i) pure Z2\mathbb{Z}_2Z2​ even and odd gauge theories, (ii) free fermions in a static background of deconfined Z2\mathbb{Z}_2Z2​ gauge fields, (iii) the kinetic Rokhsar-Kivelson quantum dimer model at a generic dimer filling. We develop a local transformation that maps the lattice gauge theory onto a model of Z2\mathbb{Z}_2Z2​ gauge-invariant spin 1/21/21/2 degrees of freedom. Using the mapping, we perform numerical density matrix renormalization group calculations that corroborate our understanding of the limits identified above. Moreover, in the absence of the magnetic plaquette term, we reveal signatures of topologically ordered Dirac semimetal and staggered Mott insulator phases at half-filling. At strong coupling, the lattice gauge theory displays fracton phenomenology with isolated fermions being completely frozen and dimers exhibiting restricted mobility. In that limit, we predict that in the ground state dimers form compact clusters, whose hopping is suppressed exponentially in their size. We determine the band structure of the smallest clusters numerically using exact diagonalization.
Constrained many-body phases in a Z2\mathbb{Z}_2Z2​-Higgs lattice gauge theory
We study the ground-state phase diagram of a one-dimensional Z2\mathbb{Z}_2Z2​ lattice gauge theory coupled to soft-core bosonic matter at unit filling, inspired by the Higgs sector of the standard model. Through a combination of analytical perturbative approaches, exact diagonalization, and density-matrix-renormalization-group simulations, we uncover a rich phase diagram driven by gauge-field-mediated resonant pair hopping and the confinement of single particles. The pair hopping results in a bunching state with superextensive energy and macroscopic particle number fluctuations at strong electric field strengths and weak on-site interactions. The bunching state crosses over into a pair superfluid phase as the on-site interaction increases, characterized by a finite superfluid density and powerlaw-decaying pair correlations. At large on-site interaction strengths and driven by effective interactions induced by the gauge constraint, the superfluid transitions into an incompressible pair Mott insulator phase. At weak field strengths and on-site interactions, we find a plasma-like region, where single bosons exhibit large short-range correlations and the ground state is composed almost equally of states with even and odd local boson occupation. The presence of a bunching state with large number fluctuations, which is difficult to study using classical numerics, motivates experimental realizations in hybrid boson-qubit quantum simulation platforms such as circuit QED, neutral atoms, and trapped ions. Our findings highlight the rich interplay between gauge fields and soft-core bosonic matter.
We investigate the interplay of quantum one-dimensional discrete Z2{\mathbb{Z}}_{2}Z2​ gauge fields and fermion matter near full filling in terms of deconfined fractionalized hole excitations that constitute mobile domain walls between vacua that break spontaneously translation symmetry. In the limit of strong string tension, we uncover emergent integrable correlated hopping dynamics of holes which is complementary to the constrained XXZ description in terms of bosonic dimers. We analyze numerically quantum dynamics of spreading of an isolated hole together with the associated time evolution of entanglement and provide analytical understanding of its salient features. We also study the model enriched with a short-range interaction and clarify the nature of the resulting ground state at low filling of holes and identify deconfined hole excitations near the hole filling ${\ensuremath{\nu}}^{h}=1/3$.
Gauge theories are of paramount importance in our understanding of fundamental constituents of matter and their interactions. However, the complete characterization of their phase diagrams and the full understanding of non-perturbative effects are still debated, especially at finite charge density, mostly due to the sign-problem affecting Monte Carlo numerical simulations. Here, we report the Tensor Network simulation of a three dimensional lattice gauge theory in the Hamiltonian formulation including dynamical matter: Using this sign-problem-free method, we simulate the ground states of a compact Quantum Electrodynamics at zero and finite charge densities, and address fundamental questions such as the characterization of collective phases of the model, the presence of a confining phase at large gauge coupling, and the study of charge-screening effects.
The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics.However, except for certain limits (for instance, a large number of flavors of matter fields), analytical methods can provide few concrete results.Here we show that the problem of compact Uð1Þ lattice gauge theory coupled to fermionic matter in ð2 þ 1ÞD is possible to access via sign-problem-free quantum Monte Carlo simulations.One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations.By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous-symmetrybreaking phases such as the valence-bond solid (VBS) and Néel antiferromagnet emerge.Deconfined phases with algebraic spin and VBS correlation functions are also observed.Such deconfined phases are incarnations of exotic states of matter, i.e., the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases.The phase transitions between the deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality.In particular, for four flavors N f ¼ 4, our data suggest a continuous quantum phase transition between the VBS and Néel order.We also provide preliminary theoretical analysis for these quantum phase transitions.