arXiv subjects

Tin Sulejmanpasic

Publications and source records attributed to Tin Sulejmanpasic.

At least 19 recordsLinked to original sources

arXiv2026

Proof of entropic order in Generalized Ising Models

Ordering at arbitrarily high temperature - entropic order - has been argued to take place in a class of generalized Ising models parameterised by a real interaction parameter $p$ when $p\ge 1$. We give a rigorous proof of this conjecture. We further show that on arbitrary graphs, these models solve graph packing problems - crucially, the Maximum Independent Set optimisation problem. Due to the NP-hardness of this packing problem on generic graphs, some lattice systems will exhibit glassy phases. We call this phenomenon $entropic$ $glass$.

cond-mat.stat-mech↗

arXiv2026

Minimal Models of Entropic Order

Due to entropic effects, it is possible that generic high-energy states of a quantum or classical system are ordered. This leads to spontaneous symmetry breaking at arbitrarily high temperatures. We present minimal models of entropic order that arise from very simple interactions. Our main examples are the Arithmetic Ising Model (AIM) and its quantum analogue, where usual Ising spins are replaced by non-negative integers. Using a large-flavor expansion together with numerical simulations, we find that the high-temperature phase is ordered in the classical and quantum models. We also introduce classical gas models whose interactions drive the system to a crystal at high temperatures.

cond-mat.stat-mech↗

arXiv2025

Emergent photons and mechanisms of confinement

We numerically study $\mathbb{Z}_N$ lattice gauge theories in 4D as prototypical models of systems with $\mathbb{Z}_N$ 1-$\textit{form symmetry}$. For $N \geq 3$, we provide evidence that such systems exhibit not only the expected phases with spontaneously broken/restored symmetry but also a third photon phase. When present, the 1-form symmetry provides a precise notion of confinement, and it is commonly believed that confinement ensues due to the proliferation of extended, string-like objects known as $\textit{center vortices}$, which carry a $\mathbb{Z}_N$ flux. However, this picture is challenged by the three-phase scenario investigated here. We show that both the confined and the photon phases are associated with the proliferation of center vortices and that the key difference between them lies in whether or not vortex-junctions - the $\textit{monopoles}$ - proliferate.

hep-lat↗

arXiv2025

Phase structure of self-dual lattice gauge theories in 4d

We discuss U(1) lattice gauge theory models based on a modified Villain formulation of the gauge action, which allows coupling to bosonic electric and magnetic matter. The formulation enjoys a duality which maps electric and magnetic sectors into each other. We propose several generalizations of the model and discuss their 't~Hooft anomalies. A particularly interesting class of theories is the one where electric and magnetic matter fields are coupled with identical actions, such that for a particular value of the gauge coupling the theory has a self-dual symmetry. The self-dual symmetry turns out to be a generator of a group which is a central extension of $\mathbb Z_4$ by the lattice translation symmetry group. The simplest case amenable to numerical simulations is the case when there is exactly one electrically and one magnetically charged boson. We discuss the phase structure of this theory and the nature of the self-dual symmetry in detail. Using a suitable worldline representation of the system we present the results of numerical simulations that support the conjectured phase diagram.

hep-th↗

arXiv2025

U(1)-gauged 2-flavor spin system in 3-D

We study a U(1)-gauged 2-component spin system in 3 dimensions. For the gauge fields we use the Villain formulation with a constraint that removes lattice monopoles and in this form couple the gauge fields to 2-component spins. We discuss the simulation strategies for this highly constraint system and present first results for the phase structure. Our preliminary Monte Carlo simulations indicate that the system undergoes a second order phase transition driven by the spin coupling. However, the correlation length critical exponent is inconsistent with the conformal bootstrap constraint for a critical (rather than multi-critical) fixed point, which forces a conclusion that the transition is likely weakly 1st order, passing close to a multi-critical point. To reliably resolve the nature of the transition, simulations on larger lattices will be necessary.

hep-lat↗

arXiv2024

Phases of theories with $\mathbb{Z}_N$ 1-form symmetry and the roles of center vortices and magnetic monopoles

We analyze the phases of theories which only have a microscopic $\mathbb{Z}_N$ 1-form symmetry, starting with a topological BF theory and deforming it in accordance with microscopic symmetry. These theories have a well-defined notion of confinement. Prototypical examples are pure $SU(N)$ gauge theories and $\mathbb{Z}_N$ lattice gauge theories. Our analysis shows that the only generic phases are in $d=2$, only the confined phase; in $d=3$, both the confined phase and the topological BF phase; and in $d=4$, the confined phase, the topological BF phase, and a phase with a massless photon. We construct a $\mathbb{Z}_N$ lattice gauge theory with a deformation which, surprisingly, produces up to $(N-1)$ photons. We give an interpretation of these findings in terms of two competing pictures of confinement -- proliferation of monopoles and proliferation of center vortices -- and conclude that the proliferation of center vortices is a necessary but insufficient condition for confinement, while that of monopoles is both necessary and sufficient.

hep-th↗

arXiv2024

Canonical quantization of lattice Chern-Simons theory

We discuss the canonical quantization of $U(1)_k$ Chern-Simons theory on a spatial lattice. In addition to the usual local Gauss law constraints, the physical Hilbert space is defined by 1-form gauge constraints implementing the compactness of the $U(1)$ gauge group, and (depending on the details of the spatial lattice) non-local constraints which project out unframed Wilson loops. Though the ingredients of the lattice model are bosonic, the physical Hilbert space is finite-dimensional, with exactly $k$ ground states on a spatial torus. We quantize both the bosonic (even level) and fermionic (odd level) theories, describing in detail how the latter depends on a choice of spin structure.

hep-th↗

arXiv2023

Remarks on QCD$_4$ with fundamental and adjoint matter

We study 4-dimensional SU(N) gauge theory with one adjoint Weyl fermion and fundamental matter - either bosonic or fermionic. Symmetries, their 't Hooft anomalies, and the Vafa-Witten-Weingarten theorems strongly constrain the possible bulk phases. The first part of the paper is dedicated to a single fundamental fermion or boson. As long as the adjoint Weyl fermion is massless, this theory always possesses a $\mathbb{Z}_{2N}^χ$ chiral symmetry, which breaks spontaneously, supporting $N$ vacua and domain walls between them for a generic mass of the matter fields. We argue, however, that the domain walls generically undergo a phase transition, and we establish the corresponding 3d gauge theories on the walls. The rest of the paper is dedicated to studying the multi-flavor fundamental matter. Here, the phases crucially depend on the ratio of the number of colors and the number of fundamental flavors. We also discuss the limiting scenarios of heavy adjoint and fundamentals, which align neatly with our current understanding of QCD and $\mathcal{N}=1$ super Yang-Mills theory.

hep-th↗

arXiv2023

Modified Villain formulation of abelian Chern-Simons theory

We formulate $U(1)_k$ Chern-Simons theory on a Euclidean spacetime lattice using the modified Villain approach. Various familiar aspects of continuum Chern-Simons theory such as level quantization, framing, the discrete 1-form symmetry and its 't Hooft anomaly, as well as the electric charge of monopole operators are manifest in our construction. The key technical ingredient is the cup product and its higher generalizations on the (hyper-)cubic lattice, which recently appeared in the literature. All unframed Wilson loops are projected out by a peculiar subsystem symmetry, leaving topological, ribbon-like Wilson loops which have the correct correlation functions and topological spins expected from the continuum theory. Our action can be obtained from a new definition of the theta term in four dimensions which improves upon previous constructions within the modified Villain approach. This bulk action coupled to background fields for the 1-form symmetry is given by the Pontryagin square, which provides anomaly inflow directly on the lattice.

hep-th↗

arXiv2023

Lattice Quantum Villain Hamiltonians: Compact scalars, $U(1)$ gauge theories, fracton models and Quantum Ising model dualities

We construct Villain Hamiltonians for compact scalars and abelian gauge theories. The Villain integers are promoted to integral spectrum operators, whose canonical conjugates are naturally compact scalars. Further, depending on the theory, these conjugate operators can be interpreted as (higher-form) gauge fields. If a gauge symmetry is imposed on these dual gauge fields, a natural constraint on the Villain operator leads to the absence of defects (e.g. vortices, monopoles,...). These lattice models therefore have the same symmetry and anomaly structure as their corresponding continuum models. Moreover they can be formulated in a way that makes the well-know dualities look manifest, e.g. a compact scalar in 2d has a T-duality, in 3d is dual to a U(1) gauge theory, etc. We further discuss the gauged version of compact scalars on the lattice, its anomalies and solution, as well as a particular limit of the gauged XY model at strong coupling which reduces to the transverse-field Ising model. The construction for higher-form gauge theories is similar. We apply these ideas to the constructions of some models which are of interest to fracton physics, in particular the XY-plaquette model and the tensor gauge field model. The XY-plaquette model in 2+1d coupled to a tensor gauge fields at strong gauge coupling is also exactly described by a transverse field quantum $J_1-J_2$ Ising model with $J_1=2J_2$, and discuss the phase structure of such models.

hep-th↗

arXiv2022

Comments on QCD$_3$ and anomalies with fundamental and adjoint matter

't Hooft anomaly matching is powerful for constraining the low energy phases of gauge theories. In 3d one common anomaly is the parity anomaly in a $T$-symmetric theory where one cannot gauge the global symmetry group without breaking the time-reversal symmetry. We find that a $T$-symmetric $\text{SU}(N)$ gauge theory with either fermionic or bosonic matter in the fundamental representation of the gauge group has a parity anomaly between the flavor group and $T$-symmetry provided that there is also a massless Majorana fermion in the adjoint representation of the gauge group. We then analyze the parity anomaly in this theory, together with the more recent mod 16 time-reversal anomaly, and give some free fermion proposals as candidates for the low energy phases consistent with the anomalies. We make brief comments about the large $N$ limit and the $\T$-broken regimes in the conclusion as well as related anomalies in 4d. }

hep-th↗

arXiv2022

Self-dual U(1) lattice field theory with a $θ$-term

We study U(1) gauge theories with a modified Villain action. Such theories can naturally be coupled to electric and magnetic matter, and display exact electric-magnetic duality. In their simplest formulation without a $θ$-term, such theories are ultra-local. We extend the discussion to U(1) gauge theories with $θ$-terms, such that $θ$ periodicity is exact for a free theory, and show that imposing electric-magnetic duality results in a local, but not ultra-local lattice action, which is reminiscent of the Lüscher construction of axial-symmetry preserving fermions in 4d. We discuss the coupling to electric and magnetic matter as well as to dyons. For dyonic matter the electric-magnetic duality and shifts of the $θ$-angle by $2π$ together generate an SL$(2,\mathbb Z)$ duality group of transformations, just like in the continuum. We finally illustrate how the SL$(2,\mathbb Z)$ duality may be used to explore theories at finite $θ$ without a sign problem.

hep-lat↗

arXiv2021

Numerical simulation of self-dual U(1) lattice field theory with electric and magnetic matter

We study a recently proposed formulation of U(1) lattice field theory with electric and magnetic matter based on the Villain formulation. This discretization allows for a duality that gives rise to relations between weak and strong gauge coupling. There exists a self-dual value of the gauge coupling where one may study the model as a function of the remaining matter coupling. Using Monte Carlo simulations based on a worldline/worldsheet representation of the system we evaluate order parameters for spontaneous breaking of self-duality. We find that in some interval of the matter coupling self-duality becomes broken spontaneously. We determine the endpoints of this interval and study the nature of the corresponding critical points. Finally we explore the system away from the self-dual gauge coupling and show that when crossing the self-dual point a first order jump is seen in the order parameters.

hep-lat↗

arXiv2021

Ising model as a $U(1)$ Lattice Gauge Theory with a $θ$-term

We discuss a gauged XY model a $θ$-term on an arbitrary lattice in 1+1 dimensions, and show that the theory reduces exactly to the 2d Ising model on the dual lattice in the limit of the strong gauge coupling, provided that the topological term is defined via the Villain action. We discuss the phase diagram by comparing the strong and weak gauge coupling limits, and perform Monte Carlo simulations at intermediate couplings. We generalize the duality to higher-dimensional Ising models using higher-form U(1) gauge field analogues.

hep-lat↗

arXiv2020

First-principle simulations of 1+1d quantum field theories at $θ=π$ and spin-chains

We present a lattice study of a 2-flavor $U(1)$ gauge-Higgs model quantum field theory with a topological term at $θ=π$. Such studies are prohibitively costly in the standard lattice formulation due to the sign-problem. Using a novel discretization of the model, along with an exact lattice dualization, we overcome the sign-problem and reliably simulate such systems. Our work provides the first ab initio demonstration that the model is in the spin-chain universality class, and demonstrates the power of the new approach to $U(1)$ gauge theories.

cond-mat.str-el↗

arXiv2020

Universality between vector-like and chiral quiver gauge theories: Anomalies and domain walls

We study low-energy dynamics of $[SU(N)]^K$ chiral quiver gauge theories in connection with $\mathcal{N}=1$ super Yang-Mills (SYM) theory, and quantum chromodynamics with bi-fundamental fermions (QCD(BF)). These theories can be obtained by $\mathbb{Z}_K$ orbifold projections of $\mathcal{N}=1$ $SU(NK)$ SYM theory, but the perturbative planar equivalence does not extend nonperturbatively for $K\ge 3$. In order to study low-energy behaviors, we analyze these systems using 't~Hooft anomaly matching and reliable semiclassics on $\mathbb{R}^3\times S^1$. Thanks to 't~Hooft anomaly that involves $1$-form center symmetry and discrete chiral symmetry, we predict that chiral symmetry must be spontaneously broken in the confinement phase, and there exist $N$ vacua. Theories with even $K$ possess a physical $θ$ angle despite the presence of massless fermions, and we further predict the $N$-branch structure associated with it; the number of vacua is enhanced to $2N$ at $θ=π$ due to spontaneous $CP$ breaking. Both of these predictions are explicitly confirmed by reliable semiclassics on $\mathbb{R}^3\times S^1$ with the double-trace deformation. Symmetry and anomaly of odd-$K$ theories are the same as those of the ${\cal N}=1$ SYM, and the ones of even-$K$ theories are same as those of QCD(BF). We unveil why there exists universality between vector-like and chiral quiver theories, and conjecture that their ground states can be continuously deformed without quantum phase transitions. We briefly discuss anomaly inflow on the domain walls connecting the vacua of the theory and possible anomaly matching scenarios.

hep-th↗

arXiv2020

Bions and Instantons in Triple-well and Multi-well Potentials

Quantum systems with multiple degenerate classical harmonic minima exhibit new non-perturbative phenomena which are not present for the double-well and periodic potentials. The simplest characteristic example of this family is the triple-well potential. Despite the fact that instantons are exact semiclassical solutions with finite and minimal action, they do not contribute to the energy spectrum at leading order in the semiclassical analysis. This is because the instanton fluctuation prefactor vanishes, which can be interpreted as the action becoming infinite quantum mechanically. Instead, the non-perturbative physics is governed by different types of {\it bion} configurations. A generalization to supersymmetric and quasi-exactly soluble models is also discussed. An interesting pattern of interference between topological and neutral bions, depending on the hidden topological angle, the discrete theta angle and the perturbative level number, leads to an intricate pattern of divergent/convergent expansions for low lying states, and provides criteria for the exact solvability of some of the states. We confirm these semiclassical bion predictions using the Bender-Wu Mathematica package to study the structure of the associated perturbative expansions. It also turns out that all the systems we study have a curious exact one-to-one relationship between the perturbative coefficients of the three wells, which we check using the BenderWu package.

hep-th↗

arXiv2019

Abelian gauge theories on the lattice: $θ$-terms and compact gauge theory with(out) monopoles

We discuss a particular lattice discretization of abelian gauge theories in arbitrary dimensions. The construction is based on gauging the center symmetry of a non-compact abelian gauge theory, which results in a Villain type action. We show that this construction has several benefits over the conventional $U(1)$ lattice gauge theory construction, such as electric-magnetic duality, natural coupling of the theory to magnetically charged matter in four dimensions, complete control over the monopoles and their charges in three dimensions and a natural $θ$-term in two dimensions. Moreover we show that for bosonic matter our formulation can be mapped to a worldline/worldsheet representation where the complex action problem is solved. We illustrate our construction by explicit dualizations of the $CP(N\!-\!1)$ and the gauge Higgs model in $2d$ with a $θ$ term, as well as the gauge Higgs model in $3d$ with constrained monopole charges. These models are of importance in low dimensional anti-ferromagnets. Further we perform a natural construction of the $θ$-term in four dimensional gauge theories, and demonstrate the Witten effect which endows magnetic matter with a fractional electric charge. We extend this discussion to $PSU(N)=SU(N)/\mathbb Z_N$ non-abelian gauge theories and the construction of discrete $θ$-terms on a cubic lattice.

hep-lat↗