Related papers: Lieb-Schultz-Mattis type theorem with higher-form …
The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's…
Scalar particles in the adjoint representation of a non-Abelian gauge theory play an important role in many scenarios beyond the standard model, especially of GUT type. For such theories manifestly gauge-invariant, massless, composite…
Can high energy physics be simulated by low-energy, non-relativistic, many-body systems, such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in…
Lattice gauge theories are a powerful language to theoretically describe a variety of strongly correlated systems, including frustrated magnets, high-$T_c$ superconductors, and topological phases. However, in many cases gauge fields couple…
Motivated by recently reported magnetic-field induced topological phases in ultracold atoms and correlated Moir\'e materials, we investigate topological phase transitions in a minimal model consisting of interacting spinless fermions…
The custodial Two-Higgs-Doublet-Model with SU(2) gauge fields is studied on the lattice. This model has the same global symmetry structure as the Standard Model but the additional Higgs field enlarges the scalar spectrum and opens the…
We study translationally invariant spin chains where each unit cell contains an $n$-state projective representation of a $\mathbb{Z}_n\times\mathbb{Z}_n$ internal symmetry, generalizing the spin-1/2 XYZ chain. Such spin chains possess a…
We discuss quantum Hall effects in a gapped insulator on a periodic two-dimensional lattice. We derive a universal relation among the the quantized Hall conductivity, and charge and flux densities per physical unit cell. This follows from…
Modulated symmetries are internal symmetries that act in a spatially non-uniform manner. Consequently, when a modulated symmetry $G_{\text{int}}$ is combined with a spatial symmetry $G_{\text{sp}}$, the total symmetry group takes the form…
An obstacle to realize supersymmetry on a lattice is the breakdown of Leibniz rule. We give a proof of a no-go theorem that it is impossible to construct a lattice field theory in an infinite lattice volume with any nontrivial field…
We present a lattice formulation of noncommutative Yang-Mills theory in arbitrary even dimensionality. The UV/IR mixing characteristic of noncommutative field theories is demonstrated at a completely nonperturbative level. We prove a…
An internal symmetry in a lattice model is said to be onsiteable if it can be disentangled into an onsite action by introducing ancillas and conjugating with a finite-depth circuit. A standard lore holds that onsiteability is equivalent to…
It is known that certain theories with extended supersymmetry can be discretized in such a way as to preserve an exact fermionic symmetry. In the simplest model of this kind, we show that this residual supersymmetric invariance is actually…
Lattice regularizations are pivotal in the non-perturbative quantization of gauge field theories. Wilson's proposal to employ group-valued link fields simplifies the regularization of gauge fields in principal fiber bundles, preserving…
We investigate the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with $U(1)$ symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model…
Lieb-Mattis theorem orders the lowest-energy states of total spin $s$ of a system of $P$ interacting fermions. We generalize these predictions to fermionic mixtures of $P$ particles with more than $N=2$ spinor components/species in the…
We construct a Hamiltonian lattice regularisation of the $N$-flavour Gross-Neveu model that manifestly respects the full $\mathsf{O}(2N)$ symmetry, preventing the appearance of any unwanted marginal perturbations to the quantum field…
Gauge theories in (1+1)D have attracted renewed attention partially due to their experimental realizations in quantum simulation platforms. In this work, we revisit the lattice massive Schwinger model and the (1+1)D lattice Abelian-Higgs…
We propose a new lattice superfield formalism in momentum representation which accommodates species doublers of the lattice fermions and their bosonic counterparts as super multiplets. We explicitly show that one dimensional N=2 model with…
We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a…