Related papers: A Unified Graph-Theoretic Framework for Free-Fermi…
We investigate dynamical symmetry breaking of the Gross-Neveu model in the light-front formalism without introducing auxiliary fields. While this system cannot have zero-mode constraints, we find that a nontrivial solution to the constraint…
The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined by Banica capturing the quantum symmetries of the graph. In…
We study a Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) space-time in the theory of $f(Q)$-gravity, where $Q$ denotes the non-metricity scalar. It has been previously shown in the literature, that there exist four distinct families of…
The worldline formalism shares with string theory the property that it allows one to write down master integrals that effectively combine the contributions of many Feynman diagrams. While at the one-loop level these diagrams differ only by…
The gravitational spin connection appears in gravity as a non-Abelian gauge field for the Lorentz group $SO(3,1)$, which is non-compact. The action for General Relativity is linear in the field strength associated to the spin connection,…
For a systematic study of charge degrees of freedom in lattices with geometric frustration, we consider spinless fermions on the checkerboard lattice with nearest-neighbor hopping $t$ and nearest-neighbor repulsion $V$ at quarter-filling.…
We investigate the generalized Hubbard model of $(2n+1)$ Fermion species interacting via a symmetric contact attraction potential. We prove that the ground state of such system is a gapless superfluid, where a full Fermi surface coexists…
Correlation functions of fermionic fields described by the massless Thirring model are analysed within the operator formalism developed by Klaiber and the path-integral approach with massless fermions quantized in the chiral symmetric…
We present an approach to solving the ground state of Fermi systems that contain spin or other discrete degrees of freedom in addition to continuous coordinates. The approach combines a Markov chain Monte Carlo sampling for energy…
A graph-theoretic method is introduced for analyzing fermion mass spectra in latticized theory-space models, including chain models arising from dimensional deconstruction. Fermion mass terms are mapped to bipartite graphs, with fields as…
The Robinson-Trautman solution in the Einstein-Maxwell-$\Lambda$ system admits a shear-free and twist-free null geodesic congruence with a nonvanishing expansion. Restricting to the case where the Maxwell field is aligned, i.e., the…
Research on topological phases of matter is a core field in modern condensed matter physics. Free fermion systems, such as topological insulators and superconductors, have been studied using the "Tenfold Way" and K-theory. Building on…
We construct entanglement renormalization schemes which provably approximate the ground states of non-interacting fermion nearest-neighbor hopping Hamiltonians on the one-dimensional discrete line and the two-dimensional square lattice.…
In 1962, Erd\H{o}s proved that if a graph $G$ with $n$ vertices satisfies $$ e(G)>\max\left\{\binom{n-k}{2}+k^2,\binom{\lceil(n+1)/2\rceil}{2}+\left\lfloor \frac{n-1}{2}\right\rfloor^2\right\}, $$ where the minimum degree $\delta(G)\geq k$…
We study the stability with respect to a broad class of perturbations of gapped ground state phases of quantum spin systems defined by frustration-free Hamiltonians. The core result of this work is a proof using the…
We derive field theory descriptions for measurement-induced phase transitions in free fermion systems. We focus on a multi-flavor Majorana chain, undergoing Hamiltonian evolution with continuous monitoring of local fermion parity operators.…
The Hamiltonian renormalisation programme motivated by constructive QFT and Osterwalder-Schrader reconstruction which was recently launched for bosonic field theories is extended to fermions. As fermion quantisation is not in terms of…
We propose a new unified theoretical framework to construct equivalent representations of the multi-state Hamiltonian operator and present several approaches for the mapping onto the Cartesian phase space. After mapping an F-dimensional…
Spin foam models are the path integral counterparts to loop quantized canonical theories. In the last few years several spin foam models of gravity have been proposed, most of which live on finite simplicial lattice spacetime. The lattice…
In this paper, a detailed analysis on normal modes of the linearized Hermite collision operator is presented, which follows from linearizing spin Boltzmann equation for massive fermions proposed in \cite{Weickgenannt:2021cuo} with the…