We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model in (1+1) dimensions using matrix product state (MPS) simulations. At zero temperature and along the symmetry line of the phase diagram, we find a sequence of inhomogeneous ground states that arise through a real-space version of the mechanism of Hilbert-space fragmentation. For weak interactions, doping the symmetry-protected topological (SPT) phase of the GNW model leads to localised charges or holes at periodic arrangements of immobile topological defects separating the fragmented subchains: a topological crystal. Increasing the interactions, we observe a transition into a paritybroken phase with a pseudoscalar condensate displaying a modulated periodic pattern. This soliton lattice is a sequence of topological charges corresponding to anti-kinks, which also bind the doped fermions at their respective centres. Out of this symmetry line, we show that quasi-spiral profiles appear with a characteristic wavevector set by the density k = 2 pi rho, providing non-perturbative evidence for chiral spirals beyond the large-N limit. These results demonstrate that various exotic inhomogeneous phases can arise in lattice field theories, and motivate the use of quantum simulators to confirm such QCD-inspired phenomena in future experiments.

The Thirring model in 2+1d with N Dirac flavors can exhibit spontaneous U(2N)→U(N)⊗U(N) breaking through fermion - antifermion condensation in the limit m→0. With no small parameter in play the symmetry-breaking dynamics is strongly-interacting and quantitative work requires a fermion formulation accurately capturing global symmetries. We present simulation results for N=1 obtained with Wilson kernel domain wall fermions on 16^3× L_s, with L_s=24,…,120. The L_s→∞ extrapolation of the bilinear condensate ⟨⟩ as a function of coupling and bare mass is fitted to an empirical equation of state; the resulting critical exponents are significantly altered from previously obtained values, and for the first time resemble those emerging from analytic predictions based on approximate solutions to Schwinger-Dyson equations, consistent with a putative UV-stable renormalisation group fixed point. To address the non-perturbative issue of the value N_c below which such a fixed point exists we present preliminary results obtained with N=2.

Motivated by ongoing interest in the universal behaviour of the Hubbard model of spinning electrons on honeycomb and π-flux lattices at the semi-metal – Mott insulator phase transition, we formulate the chiral Heisenberg model, a theory of relativistic fermions in three spacetime dimensions, as a lattice field theory using domain wall fermions. The contact interaction term preserves an SU(2) global symmetry. We perform numerical simulations using the Rational Hybrid Monte Carlo algorithm on system sizes L^3× L_s with L∈{8,…,24} and domain wall separation L_s∈{8,16,24}. We locate the phase transition corresponding to spontaneous SU(2)→U(1) breaking, yielding critical exponent estimates ν^-1=0.63(3), η_Φ=1.42(8). These values are considerably removed from estimates obtained from simulations performed in (2+1)D, ie. with the time and spatial directions treated differently, but align more closely with analytic estimates obtained using 3D covariant field theory. We also present first results for the fermion correlator, ultimately needed for the determination of the exponent η_Ψ, highlighting the need to rotate the fermion source to a common reference direction in isospace in order to obtain a signal.

We present results of a lattice field theory simulation of the (2+ 1)D Thirring model with N = 1 fermion flavors, using domain wall fermions. The model exhibits a U(2)-symmetry-breaking phase transition with the potential to define a UV-stable renormalization group fixed point. The novelty is the replacement of the Shamir kernel used in all previous work with the Wilson kernel, improving the action particularly with respect to the Ls-* 00 limit needed to recover U(2), now under much better control. Auxiliary field ensembles generated on 163 x 24 with varying self-interaction strength g2 and bare mass m are used to measure the bilinear condensate order parameter ( psii gamma 3 psi) with domain wall separations as large as Ls = 120. The resulting Ls-* 00 extrapolation is used to fit an empirical equation of state modeling spontaneous symmetry breaking as m-* 0. The fit is remarkably stable and compelling, with the fitted critical exponents beta m <^> 2.4, delta <^> 1.3 differing markedly from previous estimates. The associated susceptibility exhibits a mass hierarchy in line with physical expectations, again unlike previous estimates. Schwinger-Dyson equation (SDE) solutions of the Thirring model exploiting a hidden local symmetry in the action are reviewed and analytic predictions presented for the exponents. In contrast to all previous lattice studies, the universal characteristics of the critical point revealed qualitatively resemble the SDE predictions.

The FASTSUM collaboration has a long-standing programme of using anisotropic lattice QCD to investigate strong interaction thermodynamics, and in particular spectral quantities. Here we present first results from our new ensemble which has a temporal lattice spacing aτ=15am and anisotropy ξ=as/aτ=7, giving unprecedented resolution in the temporal direction. We show results for the chiral transition, vector–axial-vector degeneracy, and heavy quarkonium, and compare them with earlier results with coarser time resolution.

We present recent updates and results from QC_2D (Two Colour QCD) simulations at non-zero baryon density, including progress toward determining the speed of sound.

The FASTSUM Collaboration has developed a comprehensive research programme in thermal lattice QCD using 2+1 flavour ensembles. We review our recent hadron spectrum analyses of open charm mesons and charm baryons at non-zero temperature. We also detail our determination of the interquark potential in the bottomonium system using NRQCD quarks. All of our work uses anisotropic lattices where the temporal lattice spacing is considerably finer than the spatial one allowing better resolution of temporal correlation functions.

The planar Thirring model is thought to have a strongly coupled critical point for a single flavor of fermion. We look at the calculation of the bilinear condensate in this critical region, and its characterization via an equation of state. Since the computation is numerically challenging, we investigate the improved Dirac operators. We present findings on different methods of calculation using a rational hybrid Monte-Carlo scheme, and calculations of the bilinear condensate, an equation of state and the associated critical exponents. Overlap and domain wall Dirac operators, and variants therein are considered.

Ultracold Fermi gases of spin-3/2 atoms provide a clean platform to realise SO(5) models of 4-Fermi interactions in the laboratory. By confining the atoms in a two-dimensional Raman lattice, we show how this system can be used as a flexible quantum simulator of Dirac quantum field theories (QFTs) that combine Gross-Neveu and Thirring interactions with a higher-order topological twist. We show that the lattice model corresponds to a regularization of this QFT with an anisotropic twisted Wilson mass. This allows us to access higher-order topological states protected by a hidden SO(5) symmetry, a remnant of the original rotational symmetry of the 4-Fermi interactions that is not explicitly broken by the lattice discretization. Using large-$N$ methods, we show that the 4-Fermi interactions lead to a rich phase diagram with various competing fermion condensates. Our work opens a route for the implementation of correlated higher-order topological states with tunable interactions that has interesting connections to non-trivial relativistic QFTs of Dirac fermions in $D = 2 + 1$ dimensions.

The FASTSUM Collaboration has developed a comprehensive research programme in thermal QCD using 2+1 flavour, anisotropic ensembles. In this talk, we summarise some of our recent results including thermal hadron spectrum calculations using our ``Generation 2L'' ensembles which have pion masses of 239(1) MeV. These include open charm mesons and charm baryons. We also summarise our work using the Backus Gilbert approach to determining the spectral function of the NRQCD bottomonium system. Finally, we review our determination of the interquark potential in the same system, but using our ``Generation 2'' ensembles which have heavier pion masses of 384(4) MeV.

Symmetry has been at the heart of lattice field theory since its inception [...]

We employ the domain wall fermion (DWF) formulation of the Thirring model on a lattice in 2+1+1 dimensions and perform $N=1$ flavor Monte Carlo simulations. At a critical interaction strength the model features a spontaneous $\mathrm{U}(2)\rightarrow\mathrm{U}(1)\otimes \mathrm{U}(1)$ symmetry breaking; we analyse the induced spin-0 mesons, both Goldstone and non-Goldstone, as well as the correlator of the fermion quasiparticles, in both resulting phases. Crucially, we determine the anomalous dimension $\eta_\psi\approx 3$ at the critical point, in stark contrast with the Gross-Neveu model in 3$d$ and with results obtained with staggered fermions. Our numerical simulations are complemented by an analytical treatment of the free fermion correlator, which exhibits large early-time artifacts due to branch cuts in the propagator stemming from unbound interactions of the fermion with its heavy doublers. These artifacts are generalisable beyond the Thirring model, being an intrinsic property of DWF, or more generally Ginsparg-Wilson fermions.

We present some results pertaining to partially quenched formulations of the overlap/domain wall operator with the Thirring model in 2+1D. Auxiliary fields are generated with a Shamir domain wall approach and measurements of eigenvalues and condensates are contrasted with different overlap operators. The numerical challenge posed by a non-compact formulation is highlighted, and the effective use of lower accuracy sea fermions is demonstrated.

We report results of simulations of the 2 + 1d Thirring model with N fermion flavors, defined on a lattice using domain wall fermions. This approach is devised to respect as far as possible the underlying U(2N) symmetry of the continuum model, expected to be recovered in the limit wall separation Ls → ∞. For N = 1 there is a symmetry-breaking phase transition associated with bilinear condensation at strong fermion self-interaction, which is a plausible location for a quantum critical point. Fits to a renormalisation group-inspired equation of state yield critical exponents distinct from those obtained using a version of the model defined using staggered fermions.

I review the Thirring model in 2+1$d$ dimensions, focussing in particular on possible strongly-interacting UV-stable fixed points of the renormalisation group, corresponding to a continuous phase transition where a U($2N$) global symmetry spontaneously breaks to U($N)\otimes$U($N$). Since there is no small parameter in play, a systematic non-perturbative approach such as numerical simulation of lattice field theory is mandated. I compare and contrast various formulations, paying particular attention to models formulated with either staggered or domain wall lattice fermions. Domain wall fermions, which faithfully capture U($2N$) symmetry in the limit of wall separation $L_s\to\infty$, predict a critical flavor number $1

The infamous sign problem makes it impossible to probe dense (baryon density μ B > 0) QCD at temperatures near or below the deconfinement threshold. As a workaround, one can explore QCD-like theories such as twocolour QCD (QC 2 D) which don’t suffer from this sign problem but are qualitively similar to real QCD. Previous studies on smaller lattice volumes have investigated deconfinement and colour superfluid to normal matter transitions. In this study we look at a larger lattice volume N s = 24 in an attempt to disentangle finite volume and finite temperature effects. We also fit to a larger number of diquark sources to better allow for extrapolation to zero diquark source.

We determine the ground state meson masses at low temperature using simulations with $2+1$ flavours of improved Wilson-clover fermions. Subsequently we study the effect of increasing the temperature of the hadron gas, including the transition to the quark-gluon plasma, as well as the restoration of $SU(2)_A$ chiral symmetry. We use the FASTSUM anisotropic, fixed-scale Generation2L ensembles and consider mesons with light, strange and charm content.

We present the most recent results from the FASTSUM collaboration for hadron properties at high temperature. This includes the temperature dependence of the light and charmed meson and baryon spectrum, as well as properties of heavy quarkonia. The results are obtained using anisotropic lattices with a fixed scale approach. We also present the status of our next generation gauge ensembles.