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:2201.07171 · Physical Review Research

Exploring bosonic and fermionic link models on (3+1)D tubes

Debasish Banerjee, Emilie Huffman, Lukas Rammelmüller

Published Sep 2, 2022• 7 citations
arXivHTMLPDF

Abstract

Quantum link models have attracted a lot of attention in recent times as a generalization of Wilson's lattice gauge theories, and are particularly suitable for realization on quantum simulators and computers. These models are known to host new phases of matter and act as a bridge between particle and condensed matter physics. In this paper, we study the Abelian $\text{U}(1)$ lattice gauge theory in $(3+1)\mathrm{D}$ tubes using large-scale exact diagonalization. We are then able to motivate the phase diagram of the model with finite-size scaling techniques, and in particular propose the existence of a Coulomb phase. Furthermore, we introduce models involving fermionic quantum links, which generalize the gauge degrees of freedom to be of fermionic nature. We prove that while the spectra remain identical between the bosonic and the fermionic versions of the $\text{U}(1)$-symmetric quantum link models in $(2+1)\mathrm{D}$, they are different in $(3+1)\mathrm{D}$. We discuss the prospects of realizing the magnetic field interactions as correlated hopping in quantum simulator experiments.

DOI
10.1103/physrevresearch.4.033174

Related papers

Bosonic vs. Fermionic Matter in Quantum Simulations of $2+1$D Gauge Theories

N. S. Srivatsa, Jesse J. Osborne, Debasish Banerjee +1 more

Quantum link models extend lattice gauge theories beyond the traditional Wilson formulation and present promising candidates for both digital and analog quantum simulations. Fermionic matter coupled to $U(1)$ quantum link gauge fields has been extensively studied, revealing a phase diagram that includes transitions from the columnar phase in the quantum dimer model to the resonating valence bond phase in the quantum link model, potentially passing through a disordered liquid-like phase. In this study, we investigate the model coupled to hardcore bosons and identify a similar phase structure, though with a more intricate mixture of phases around the transition. Our analysis reveals that near the transition region, a narrow and distinct ordered phase emerges, characterized by gauge fields forming plaquette configurations with alternating orientations, which is then followed by a thinner, liquid-like regime. This complexity primarily stems from the differences in particle statistics, which manifest prominently when the matter degrees of freedom become dynamic. Notably, our findings suggest that bosons can effectively replace fermions in lattice gauge theory simulations, offering solutions to the challenges posed by fermions in both digital and analog quantum simulations.

arXiv:2504.17000•Apr 23, 2025•0 citations

Towards the phase diagram of fermions coupled with $SO(3)$ quantum links in (2 + 1)−D

Graham Van Goffrier, Debasish Banerjee, Bipasha Chakraborty +2 more

Quantum link models (QLMs) are generalizations of Wilson’s lattice gauge theory formulated with finite-dimensional link Hilbert spaces. In certain cases, the non-Abelian Gauss Law constraint can be exactly solved, and the gauge invariant subspace embedded onto local spin Hamiltonians for efficient quantum simulation. In (1 + 1)D previous studies of the SO(3) QLM coupled to adjoint fermionic matter have been shown to reflect key properties of QCD and nuclear physics, including distinct confining/deconfining phases and hadronic bound states. We extend the model to (2 + 1)D dimensions for the first time, and report on our initial results. We review the construction of gauge-invariant state space for the proposed models, and study the single-plaquette ground state via exact-diagonalisation. We provide indications of a rich phase diagram which shows both spontaneous and explicit chiral symmetry breaking, confinement, and distinct magnetic phases characterised by different plaquette expectation values.

arXiv:2412.09691•International Symposium on Lattice Field Theory (LATTICE)•Feb 15, 2025•0 citations

Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d

Tomohiro Hashizume, Jad C. Halimeh, Philipp Hauke +1 more

The exploration of phase diagrams of strongly interacting gauge theories coupled to matter in lower dimensions promises the identification of exotic phases and possible new universality classes, and it facilitates a better understanding of salient phenomena in Nature, such as confinement or high-temperature superconductivity. The emerging new techniques of quantum synthetic matter experiments as well as efficient classical computational methods with matrix product states have been extremely successful in one spatial dimension, and are now motivating such studies in two spatial dimensions. In this work, we consider a \mathrm{U}(1) U ( 1 ) quantum link lattice gauge theory where the gauge fields, represented by spin- \frac{1}{2} 1 2 operators are coupled to a single flavor of staggered fermions. Using matrix product states on infinite cylinders with increasing diameter, we conjecture its phase diagram in (2+1) ( 2 + 1 ) -d. This model allows us to smoothly tune between the \mathrm{U}(1) U ( 1 ) quantum link and the quantum dimer models by adjusting the strength of the fermion mass term, enabling us to connect to the well-studied phases of those models. Our study reveals a rich phase diagram with exotic phases and interesting phase transitions to a potential liquid-like phase. It thus furthers the collection of gauge theory models that may guide future quantum-simulation experiments.

arXiv:2112.00756•SciPost Physics•Aug 12, 2022•0 citations

Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d

Tomohiro Hashizume

The exploration of phase diagrams of strongly interacting gauge theories coupled to matter in lower dimensions promises the identification of exotic phases and possible new universality classes, and it facilitates a better understanding of salient phenomena in Nature, such as confinement or high-temperature superconductivity. The emerging new techniques of quantum synthetic matter experiments as well as efficient classical computational methods with matrix product states have been extremely successful in one spatial dimension, and are now motivating such studies in two spatial dimensions. In this work, we consider a $\mathrm{U}(1)$ quantum link lattice gauge theory where the gauge fields, represented by spin-$\frac{1}{2}$ operators are coupled to a single flavor of staggered fermions. Using matrix product states on infinite cylinders with increasing diameter, we conjecture its phase diagram in $(2+1)$-d. This model allows us to smoothly tune between the $\mathrm{U}(1)$ quantum link and the quantum dimer models by adjusting the strength of the fermion mass term, enabling us to connect to the well-studied phases of those models. Our study reveals a rich phase diagram with exotic phases and interesting phase transitions to a potential liquid-like phase. It thus furthers the collection of gauge theory models that may guide future quantum-simulation experiments.

•Aug 1, 2022•13 citations

From quantum link models to D-theory: a resource efficient framework for the quantum simulation and computation of gauge theories

U.‐J. Wiese

Quantum link models provide an extension of Wilson's lattice gauge theory in which the link Hilbert space is finite-dimensional and corresponds to a representation of an embedding algebra. In contrast to Wilson's parallel transporters, quantum links are intrinsically quantum degrees of freedom. In D-theory, these discrete variables undergo dimensional reduction, thus giving rise to asymptotically free theories. In this way [Formula: see text] [Formula: see text] models emerge by dimensional reduction from [Formula: see text] [Formula: see text] quantum spin ladders, the [Formula: see text] confining [Formula: see text] gauge theory emerges from the Abelian Coulomb phase of a [Formula: see text] quantum link model, and [Formula: see text] QCD arises from a non-Abelian Coulomb phase of a [Formula: see text] [Formula: see text] quantum link model, with chiral quarks arising naturally as domain wall fermions. Thanks to their finite-dimensional Hilbert space and their economical mechanism of reaching the continuum limit by dimensional reduction, quantum link models provide a resource efficient framework for the quantum simulation and computation of gauge theories. This article is part of the theme issue 'Quantum technologies in particle physics'.

arXiv:2107.09335•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Dec 20, 2021•44 citations

Perspectives on Quantum Sensing and Computation for Particle Physics

U.‐J. Wiese

<!--HTML-->Quantum link models provide an extension of Wilson's lattice gauge theory in which the link variables have operator-valued entries. For example, in a U(1) quantum link model the link variables are raising and lowering operators of quantum spins that belong to a link-based SU(2) embedding algebra. For non-Abelian SU(N), Spin(N), or Sp(N) quantum link models, the embedding algebras are SU(2N), Spin(2N), and Sp(2N), respectively. In contrast to Wilson's framework, quantum link models can be realized in a finite-dimensional link Hilbert space corresponding to a representation of the embedding algebra. This is well suited for a resource efficient implementation of quantum link models in quantum simulation experiments. The quantum link dynamics can be embodied with a finite number of well-controlled states of ultra-cold matter, including atoms in an optical lattice, ions in a trap, or quantum circuits. For example, using dual variables, a densely encoded quantum circuit has recently been constructed for a (2+1)-d U(1) quantum link model on a triangular lattice that shows qualitatively new nematic phases with rich confining dynamics. Quantum spins and quantum links are discrete quantum variables which give rise to collective low-energy excitations. In (2+1)-d, SU(N) quantum spins give rise to massless Goldstone bosons which undergo dimensional reduction to (1+1)-d asymptotically free CP(N-1) models. This can be realized in quantum simulation experiments with alkaline-earth atoms in an optical lattice. In (3+1)-d, Abelian quantum links give rise to massless photons which undergo dimensional reduction to (2+1)-d confining U(1) gauge theory, which can be embodied with spin-ice. In (4+1)-d, non-Abelian quantum links give rise to massless gluons which undergo dimensional reduction to (3+1)-d Yang-Mills theory. Quarks are naturally included as domain wall fermions. The dimensional reduction of discrete quantum variables defines D-theory, in which quantum field theories emerge from a minimal set of degrees of freedom, thus enabling resource efficient implementations in quantum simulation experiments. D-theory provides a concrete vision how to realize the ultimate long-term goal of quantum simulating QCD.

•Jan 1, 2021•0 citations
Quantum link models have attracted a lot of attention in recent times as a generalization of Wilson's lattice gauge theories, and are particularly suitable for realization on quantum simulators and computers. These models are known to host new phases of matter and act as a bridge between particle and condensed matter physics. In this paper, we study the Abelian U(1)\text{U}(1)U(1) lattice gauge theory in (3+1)D(3+1)\mathrm{D}(3+1)D tubes using large-scale exact diagonalization. We are then able to motivate the phase diagram of the model with finite-size scaling techniques, and in particular propose the existence of a Coulomb phase. Furthermore, we introduce models involving fermionic quantum links, which generalize the gauge degrees of freedom to be of fermionic nature. We prove that while the spectra remain identical between the bosonic and the fermionic versions of the U(1)\text{U}(1)U(1)-symmetric quantum link models in (2+1)D(2+1)\mathrm{D}(2+1)D, they are different in (3+1)D(3+1)\mathrm{D}(3+1)D. We discuss the prospects of realizing the magnetic field interactions as correlated hopping in quantum simulator experiments.
Bosonic vs. Fermionic Matter in Quantum Simulations of 2+12+12+1D Gauge Theories
Quantum link models extend lattice gauge theories beyond the traditional Wilson formulation and present promising candidates for both digital and analog quantum simulations. Fermionic matter coupled to U(1)U(1)U(1) quantum link gauge fields has been extensively studied, revealing a phase diagram that includes transitions from the columnar phase in the quantum dimer model to the resonating valence bond phase in the quantum link model, potentially passing through a disordered liquid-like phase. In this study, we investigate the model coupled to hardcore bosons and identify a similar phase structure, though with a more intricate mixture of phases around the transition. Our analysis reveals that near the transition region, a narrow and distinct ordered phase emerges, characterized by gauge fields forming plaquette configurations with alternating orientations, which is then followed by a thinner, liquid-like regime. This complexity primarily stems from the differences in particle statistics, which manifest prominently when the matter degrees of freedom become dynamic. Notably, our findings suggest that bosons can effectively replace fermions in lattice gauge theory simulations, offering solutions to the challenges posed by fermions in both digital and analog quantum simulations.
Towards the phase diagram of fermions coupled with SO(3)SO(3)SO(3) quantum links in (2 + 1)−D
Quantum link models (QLMs) are generalizations of Wilson’s lattice gauge theory formulated with finite-dimensional link Hilbert spaces. In certain cases, the non-Abelian Gauss Law constraint can be exactly solved, and the gauge invariant subspace embedded onto local spin Hamiltonians for efficient quantum simulation. In (1 + 1)D previous studies of the SO(3) QLM coupled to adjoint fermionic matter have been shown to reflect key properties of QCD and nuclear physics, including distinct confining/deconfining phases and hadronic bound states. We extend the model to (2 + 1)D dimensions for the first time, and report on our initial results. We review the construction of gauge-invariant state space for the proposed models, and study the single-plaquette ground state via exact-diagonalisation. We provide indications of a rich phase diagram which shows both spontaneous and explicit chiral symmetry breaking, confinement, and distinct magnetic phases characterised by different plaquette expectation values.
Ground-state phase diagram of quantum link electrodynamics in (2+1)(2+1)(2+1)-d
The exploration of phase diagrams of strongly interacting gauge theories coupled to matter in lower dimensions promises the identification of exotic phases and possible new universality classes, and it facilitates a better understanding of salient phenomena in Nature, such as confinement or high-temperature superconductivity. The emerging new techniques of quantum synthetic matter experiments as well as efficient classical computational methods with matrix product states have been extremely successful in one spatial dimension, and are now motivating such studies in two spatial dimensions. In this work, we consider a \mathrm{U}(1) U ( 1 ) quantum link lattice gauge theory where the gauge fields, represented by spin- \frac{1}{2} 1 2 operators are coupled to a single flavor of staggered fermions. Using matrix product states on infinite cylinders with increasing diameter, we conjecture its phase diagram in (2+1) ( 2 + 1 ) -d. This model allows us to smoothly tune between the \mathrm{U}(1) U ( 1 ) quantum link and the quantum dimer models by adjusting the strength of the fermion mass term, enabling us to connect to the well-studied phases of those models. Our study reveals a rich phase diagram with exotic phases and interesting phase transitions to a potential liquid-like phase. It thus furthers the collection of gauge theory models that may guide future quantum-simulation experiments.
Ground-state phase diagram of quantum link electrodynamics in (2+1)(2+1)(2+1)-d
The exploration of phase diagrams of strongly interacting gauge theories coupled to matter in lower dimensions promises the identification of exotic phases and possible new universality classes, and it facilitates a better understanding of salient phenomena in Nature, such as confinement or high-temperature superconductivity. The emerging new techniques of quantum synthetic matter experiments as well as efficient classical computational methods with matrix product states have been extremely successful in one spatial dimension, and are now motivating such studies in two spatial dimensions. In this work, we consider a U(1)\mathrm{U}(1)U(1) quantum link lattice gauge theory where the gauge fields, represented by spin-12\frac{1}{2}21​ operators are coupled to a single flavor of staggered fermions. Using matrix product states on infinite cylinders with increasing diameter, we conjecture its phase diagram in (2+1)(2+1)(2+1)-d. This model allows us to smoothly tune between the U(1)\mathrm{U}(1)U(1) quantum link and the quantum dimer models by adjusting the strength of the fermion mass term, enabling us to connect to the well-studied phases of those models. Our study reveals a rich phase diagram with exotic phases and interesting phase transitions to a potential liquid-like phase. It thus furthers the collection of gauge theory models that may guide future quantum-simulation experiments.
Quantum link models provide an extension of Wilson's lattice gauge theory in which the link Hilbert space is finite-dimensional and corresponds to a representation of an embedding algebra. In contrast to Wilson's parallel transporters, quantum links are intrinsically quantum degrees of freedom. In D-theory, these discrete variables undergo dimensional reduction, thus giving rise to asymptotically free theories. In this way [Formula: see text] [Formula: see text] models emerge by dimensional reduction from [Formula: see text] [Formula: see text] quantum spin ladders, the [Formula: see text] confining [Formula: see text] gauge theory emerges from the Abelian Coulomb phase of a [Formula: see text] quantum link model, and [Formula: see text] QCD arises from a non-Abelian Coulomb phase of a [Formula: see text] [Formula: see text] quantum link model, with chiral quarks arising naturally as domain wall fermions. Thanks to their finite-dimensional Hilbert space and their economical mechanism of reaching the continuum limit by dimensional reduction, quantum link models provide a resource efficient framework for the quantum simulation and computation of gauge theories. This article is part of the theme issue 'Quantum technologies in particle physics'.
<!--HTML-->Quantum link models provide an extension of Wilson's lattice gauge theory in which the link variables have operator-valued entries. For example, in a U(1) quantum link model the link variables are raising and lowering operators of quantum spins that belong to a link-based SU(2) embedding algebra. For non-Abelian SU(N), Spin(N), or Sp(N) quantum link models, the embedding algebras are SU(2N), Spin(2N), and Sp(2N), respectively. In contrast to Wilson's framework, quantum link models can be realized in a finite-dimensional link Hilbert space corresponding to a representation of the embedding algebra. This is well suited for a resource efficient implementation of quantum link models in quantum simulation experiments. The quantum link dynamics can be embodied with a finite number of well-controlled states of ultra-cold matter, including atoms in an optical lattice, ions in a trap, or quantum circuits. For example, using dual variables, a densely encoded quantum circuit has recently been constructed for a (2+1)-d U(1) quantum link model on a triangular lattice that shows qualitatively new nematic phases with rich confining dynamics. Quantum spins and quantum links are discrete quantum variables which give rise to collective low-energy excitations. In (2+1)-d, SU(N) quantum spins give rise to massless Goldstone bosons which undergo dimensional reduction to (1+1)-d asymptotically free CP(N-1) models. This can be realized in quantum simulation experiments with alkaline-earth atoms in an optical lattice. In (3+1)-d, Abelian quantum links give rise to massless photons which undergo dimensional reduction to (2+1)-d confining U(1) gauge theory, which can be embodied with spin-ice. In (4+1)-d, non-Abelian quantum links give rise to massless gluons which undergo dimensional reduction to (3+1)-d Yang-Mills theory. Quarks are naturally included as domain wall fermions. The dimensional reduction of discrete quantum variables defines D-theory, in which quantum field theories emerge from a minimal set of degrees of freedom, thus enabling resource efficient implementations in quantum simulation experiments. D-theory provides a concrete vision how to realize the ultimate long-term goal of quantum simulating QCD.