Disorder-free localization has been proposed as a mechanism for ergodicity breaking in lattice gauge theories (LGTs) which can even occur in two spatial dimensions (2D). It has been shown that the U(1) quantum link model (QLM) can localize due to an emergent classical percolation transition fragmenting the system into disconnected real-space clusters. While the nature of the quantum localization transition (QLT) is still debated for conventional many-body localization, here we provide a comprehensive characterization of the QLT for the QLM in 2D for a disorder-free case. In this Letter we find compelling evidence that the QLT in the 2D QLM is continuous and we determine its universality class. We base our considerations on a spectral analysis of finite-size clusters in the percolation problem which exhibits two regimes---one in which large clusters effectively behave nonergodically, a result naturally accounted for as an interference phenomenon in configuration space, and the other in which all large clusters behave ergodically. Our analysis can also be applied to other 2D U(1) LGTs potentially including also matter degrees of freedom.Disorder-free localization has been proposed as a mechanism for ergodicity breaking in lattice gauge theories (LGTs) which can even occur in two spatial dimensions (2D). It has been shown that the U(1) quantum link model (QLM) can localize due to an emergent classical percolation transition fragmenting the system into disconnected real-space clusters. While the nature of the quantum localization transition (QLT) is still debated for conventional many-body localization, here we provide a comprehensive characterization of the QLT for the QLM in 2D for a disorder-free case. In this Letter we find compelling evidence that the QLT in the 2D QLM is continuous and we determine its universality class. We base our considerations on a spectral analysis of finite-size clusters in the percolation problem which exhibits two regimes---one in which large clusters effectively behave nonergodically, a result naturally accounted for as an interference phenomenon in configuration space, and the other in which all large clusters behave ergodically. Our analysis can also be applied to other 2D U(1) LGTs potentially including also matter degrees of freedom.

arXiv:2203.06198Physical review. B./Physical review. BAug 26, 202222 citations

Interplay of Gauss Law and the Fermion Sign Problem in Quantum Link Models with Dynamical Matter

Anonymous, Debasish Banerjee, Emilie Huffman

Quantum Link Models with dynamical matter coupled to spin- $\frac{1}{2} \ \rm U(1)$ gauge fields in $d=2+1 $ and $3+1$ 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.Quantum Link Models with dynamical matter coupled to spin-$\frac{1}{2} \ \rm U(1)$ gauge fields in $d=2+1 $ and $3+1$ 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.

International Symposium on Lattice Field Theory (LATTICE)Jul 15, 20260 citations

Cluster algorithms for anisotropic quantum spin models

Naoki Kawashima

arXiv:cond-mat/9506075Journal of Statistical PhysicsJan 1, 199622 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

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.