can potentially give rise to the Coulomb phase expected in quantum electrodynamics (QED) and other confining phases. Using exact diagonalization techniques, we show that the ground state in a class of models without the magnetic field always lies in the sector which satisfies

(G_e,G_o) = (d,\ -d)

, where

d

is the spatial dimension and

e

and

o

are even and odd sites. It can be analytically proven that this sector is free of the fermion sign problem. We also demonstrate that a meron cluster algorithm for the problem naturally samples the ground states of the Hamiltonian in the aforementioned Gauss Law sector.

DOI: 10.22323/1.518.0155

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Ground-state phase diagram of quantum link electrodynamics in $(2+1)$ -dGround-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.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, 202213 citations

Quantum Link Models with dynamical matter coupled to spin-

\frac{1}{2} \ \rm U(1)

gauge fields in

d=2+1

and

3+1

(G_e,G_o) = (d,\ -d)

, where

d

is the spatial dimension and

e

and

o

Quantum Link Models with dynamical matter coupled to spin-

\frac{1}{2} \ \rm U(1)

gauge fields in $d=2+1 $ and

3+1

(G_e,G_o) = (d,\ -d)

, where

d

is the spatial dimension and

e

and

o

\frac{1}{2}

quantum links coupled to a single flavour of staggered fermions samples only two of the exponentially many Gauss law (GL) sectors at low temperatures, allowing the simulation of those two GL sectors at zero temperature in polynomial time. In this article, we analytically identify GL sectors which can be simulated without encountering the fermion sign problem in arbitrary spatial dimensions. Using large-scale exact diagonalization and cluster Monte Carlo methods, we explore the nature of phases in the GL sectors dominating at zero temperature. The ground state lives in a superselection sector free of the sign problem, and maps to the quantum dimer model with mobile monomers. The usual zero-charge GL sector suffers from the fermion sign problem, and maps to the fully packed loop model with mobile monomers. The role of the magnetic energy in causing transitions between GL sectors is outlined. We expect our results to be valid for truncated Kogut-Susskind gauge theories, beyond quantum link models.

Towards the phase diagram of fermions coupled with

SO(3)

quantum links in (2 + 1)−D

Ground-state phase diagram of quantum link electrodynamics in

(2+1)

-d

Ground-state phase diagram of quantum link electrodynamics in

(2+1)

-d

\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.