We investigate the finite-density phase diagram of a non-abelian SU(2) lattice gauge theory in (1+1) -dimensions using tensor network methods. We numerically characterise the phase diagram as a function of the matter filling and of the matter-field coupling, identifying different phases, some of them appearing only at finite densities. For weak matter-field coupling we find a meson BCS liquid phase, which is confirmed by second-order analytical perturbation theory. At unit filling and for strong coupling, the system undergoes a phase transition to a charge density wave of single-site (spin-0) mesons via spontaneous chiral symmetry breaking. At finite densities, the chiral symmetry is restored almost everywhere, and the meson BCS liquid becomes a simple liquid at strong couplings, with the exception of filling two-thirds, where a charge density wave of mesons spreading over neighbouring sites appears. Finally, we identify two tri-critical points between the chiral and the two liquid phases which are compatible with a SU(2)2 Wess-Zumino-Novikov-Witten model. Here we do not perform the continuum limit but we explicitly address the global U(1) charge conservation symmetry.
We investigate the finite-density phase diagram of a non-abelian SU(2) lattice gauge theory in (1+1) -dimensions using tensor network methods. We numerically characterise the phase diagram as a function of the matter filling and of the matter-field coupling, identifying different phases, some of them appearing only at finite densities. For weak matter-field coupling we find a meson BCS liquid phase, which is confirmed by second-order analytical perturbation theory. At unit filling and for strong coupling, the system undergoes a phase transition to a charge density wave of single-site (spin-0) mesons via spontaneous chiral symmetry breaking. At finite densities, the chiral symmetry is restored almost everywhere, and the meson BCS liquid becomes a simple liquid at strong couplings, with the exception of filling two-thirds, where a charge density wave of mesons spreading over neighbouring sites appears. Finally, we identify two tri-critical points between the chiral and the two liquid phases which are compatible with a SU(2)2 Wess-Zumino-Novikov-Witten model. Here we do not perform the continuum limit but we explicitly address the global U(1) charge conservation symmetry.
We numerically simulate a non-Abelian lattice gauge theory in two spatial dimensions, with tensor networks (TN), up to intermediate sizes ( > 30 matter sites) well beyond exact diagonalization. We focus on the SU(2) Yang-Mills model in Hamiltonian formulation, with dynamical matter and minimally truncated gauge field (hardcore gluon). Thanks to the TN sign-problem-free approach, we characterize the phase diagram of the model at zero and finite baryon number as a function of the quark bare mass and color charge. At intermediate system sizes, we detect a liquid phase of quark-pair bound-state quasiparticles (baryons), whose mass is finite towards the continuum limit. Interesting phenomena arise at the transition boundary where color-electric and color-magnetic terms are maximally frustrated: For low quark masses, we see traces of potential deconfinement, while for high masses, signatures of a possible topological order. Published by the American Physical Society 2024
We introduce the \emph{flavoured lattice Schwinger model}, a (1+1)-dimensional U(1) lattice gauge theory in which the fermion doubling problem is resolved by staggering a Z2 flavour degree of freedom rather than staggering chirality. Unlike the standard approaches, this construction preserves an exact axial U(1) symmetry at finite lattice spacing. We derive the continuum limit, showing that the model reduces to the \emph{two-flavour} massless Schwinger model, with flavours α∈{0,1} sharing one dynamical U(1) gauge field. The central result is a well-defined, regularised, gauge-invariant lattice axial charge QGA whose continuum non-conservation ⟨dQGA/dt⟩=−(2g/π)∫dx⟨E(x)⟩ arises as a direct dynamical consequence of minimal gauge coupling. A particle-hole transformation on the χ flavour exposes a hidden UL(2)×UR(2) chiral symmetry; non-Abelian bosonisation then identifies the model with a massive abelian Schwinger sector tensored with the level-1SU(2) Wess--Zumino--Witten model. Finally, we show that embedding the flavoured fermions in a ribbon-shaped (2+1)D Bernevig--Hughes--Zhang topological insulator and gauging the bulk in a constant background field factorises the boundary theory into \emph{two decoupled} single-flavour Schwinger models, one on each edge, identifying the lattice factor of 2 as one quantum of Schwinger anomaly per edge.
We perform a zero temperature analysis of a non-Abelian lattice gauge model corresponding to an SU(3) Yang-Mills theory in 1+1D at low energies. Specifically, we characterize the model ground states via gauge-invariant matrix product states, identifying its phase diagram at finite density as a function of the matter-gauge interaction coupling, the quark filling, and their bare mass. Overall, we observe an extreme robustness of baryons: For positive free-field energy couplings, all detected phases exhibit colorless quasiparticles, a strong numerical hint that QCD does not deconfine in 1D. Additionally, we show that, having access to finite-density properties, it is possible to study the stability of composite particles, including multibaryon bound states such as the deuteron.
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.
Quantum Phase Diagram of the 2+1D Untruncated SU(2) Lattice Gauge Theory with Dynamical Fermions
Non-Abelian gauge theories with dynamical matter govern the strong interaction and a broad class of strongly correlated quantum systems, yet their ground-state properties remain difficult to obtain from first principles. Using a continuous-group variational Monte Carlo approach that retains the full SU(2) gauge field without truncation, we determine the ground-state behavior of the SU(2) lattice gauge theory with staggered fermions on an L×L square lattice. Treating the magnetic and electric couplings λ and g2 independently, we find a magnetic-flux transition at λ∗=−0.040±0.005, with no resolvable drift of the transition point as the electric coupling is varied. Along the physical coupling line λ=4/g2, for L=4,6,8, we uncover a gauge-matter delocalization crossover from a flux-disordered regime at strong electric coupling to an ordered unity-flux regime at weak coupling. The chiral condensate, a gauge-invariant Wilson-line meson correlator, and the local color density consistently reveal the emergence of coherent gauge-assisted matter dynamics. Together, these results provide a unified physical picture of how magnetic-flux ordering and fermionic coherence develop in an untruncated non-Abelian lattice gauge theory.
Abstract 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.