Emergent Gauge Theories: Bridging Quantum Matter, Quantum Information, and Fundamental Interactions

Quantum systems with long-range interactions enhance the effective connectivity of a system without changing its spatial dimensionality, leading to nontrivial many-body phenomena. Motivated by this, we study a spin-1 chain with unfrustrated RKKY-like longrange exchange interactions $J(r)\sim (-1)^{r-1} r^{-\alpha}$, which naturally arise in several quantum simulation platforms. Using quantum Monte Carlo (QMC) simulations, we find that tuning the interaction exponent (\alpha) drives a transition between the symmetry-protected topological (SPT) Haldane phase and an antiferromagnetically ordered phase exhibiting true long-range order. The transition occurs near $\alpha_c = 1.22$, as identified from crossings of correlation-length ratios. Finite-size scaling collapses of the staggered structure factor and the non-local string order parameter yield a consistent correlation-length exponent $\nu = 1.0(8)$, indicating a continuous quantum critical point separating the two phases. To further probe the universal properties of the transition, we compute the Rényi entanglement entropy using replica quantum Monte Carlo simulations combined with the non-equilibrium work protocol introduced by J. K. De Mídio[1], which allows efficient estimation of entanglement entropies within QMC simulations. This approach will allow us to extract the central charge and characterize the universality class of the critical point. Our results highlight how long-range interactions influence phase transitions between topological and symmetry-broken phases in low-dimensional quantum systems. [1] J. D'Emidio, Phys. Rev. Lett. 124, 110602 (2020).

Dynamical heterogeneity, fractality, and topology are central concepts in modern condensed matter physics. Their origin is typically rooted in very different physical settings and microscopic mechanisms, such as glassy dynamics, quenched disorder and the absence of symmetry breaking. We show here that a simple, clean lattice model -- in thermal equilibrium -- hosts all three simultaneously. The dynamical heterogeneity even persists across a thermal phase transition into a long-range ordered nematic phase. Investigating the dynamics of the ordered phase, we find that the motion of its fractionalized quasiparticles is restricted to an emergent fractal network, leading to subdiffusive yet ergodic transport that deviates from conventional hydrodynamic expectations. The fractal exhibits critical scaling from the lattice scale up to long-wavelengths. This fractal structure also shapes the distribution of quasiparticle lifetimes, enhancing short-time dynamics. We discuss how this subdiffusive behavior can be probed experimentally in candidate materials through the power spectral density of the magnetization. Indeed, our results account for recent experimental results on dynamical heterogeneity in the spin ice compound $\mathrm{Dy_2Ti_2O_7}$ [arXiv:2408.00460] by identifying generation recombination noise of its fractionalized quasiparticles as the cause of dynamical heterogeneity. Our results show that dynamical heterogeneity can act as a diagnostic of new cooperative regimes, helping to transcend naive boundaries between equilibrium and non-equilibrium physics and between order and disorder.

Motivated by recent observations of fractional Chern insulators (FCIs) in the vicinity of superconducting (SC) phases (e.g. $\text{MoTe_2}$), we study fractional quantum (anomalous) Hall-superconductor heterostructures in the presence of U(1) order-parameter fluctuations and particularly focus on the case of $\nu=2/3$ quantum Hall states leading to $Z_3$ parafermions. While the emergence of $Z_3$ parafermions has already been demonstrated in the spin-unpolarized Halperin State, we demonstrate how disorder can also stabilize $ Z_3$ parafermions in the spin-polarized $nu=2/3$ state, which is expected to be present in $\text{MoTe_2}$. Due to a broad phase transition between the FCI and the superconducting state, we further study the effect of phase fluctuations on the $Z_3$ parafermions, using field-theoretical methods as well as the density-matrix renormalization group. We find a rich phase diagram composed of Mott insulating phases and two distinct Luttinger liquids, whose fundamental excitations carry charges 2e and 2e/3, respectively. In agreement with analytical considerations using conformal field theory, we numerically find transitions of Berezinskii-Kosterlitz-Thouless (BKT) type as well as a continuous $Z_3\times\text{U(1)}$ second-order phase transition characterized by central charge c = 9/5.

Topologically ordered/Long-range entangled phases of matter have been hard to unambiguously detect of due to the lack of a general observable order parameter. As a consequence, most experimental effort is focused either on interferometry of low-lying excitations or simulating the wavefunction on very small lattices and obtaining information theoretic measures from multiple wavefunction snapshots. I will present a different approach which allows one to extract an order parameter from the ground state in toy models of two dimensional topological order with boundaries, based on their quantum loop gas description. Our construction uses a combination of the unique structure of the superposition in the quantum loop gas description and the corresponding connection to the critical classical loop models to extract a universal quantity from the topologically ordered ground state. I shall discuss the extent to which the universal quantity obtained describes the anyon content of the underlying topological order, and its robustness as compared to other information theoretic quantities.

A side-coupled Majorana zero mode in Kondo systems realizes a simple yet nontrivial hybridization that profoundly alters the low-energy physics, making such setups promising candidates for detecting Majorana zero modes. Recently, we demonstrated that the low-energy behavior of this system can be captured by a spin-charge-entangled screening process with an $A\otimes N$ boundary condition. Here, we investigate the evolution of both the screening cloud and the boundary condition in the presence of competing terms that could break either the spin-charge-entangled $SU_L(2)$ rotation symmetry or the topological degeneracy. We introduce a temperature-dependent spatial integral of the screening cloud, which can be obtained from the numerical renormalization group. This quantity serves as a proper observable that unambiguously captures the properties of the screening process across temperatures. A clear crossover from conventional Kondo spin screening to spin-charge-entangled screening is observed. Taking into account the overlap between Majorana zero modes, the $A\otimes N$ boundary condition reduces to a normal one, yet the spin-charge-entangled screening is protected by the $SU_L(2)$ symmetry. On the other hand, perturbation that breaks the $SU_L(2)$ symmetry can destroy the screening singlet, while leaving the low-temperature $A\otimes N$ boundary condition intact.

Nanobubbles wield significant influence over the electronic properties of 2D materials, showing diverse applications ranging from flexible devices to strain sensors. Here, we reveal that a strongly-correlated phenomenon, i.e., Kondo resonance, naturally takes place as an intrinsic property of graphene nanobubbles. The localized strain within the nanobubbles engenders pseudo magnetic fields, driving pseudo Landau levels with degenerate Landau orbits. Under the Coulomb repulsion, the Landau orbits form an effective $SU(N)$ pseudospin coupled to the bath via exchange interaction. This results in a new flavor screening mechanism that drives an exotic flavor-frozen Kondo effect, which is absent in conventional Kondo systems. The resonance here also exhibits an unparalleled tunability via strain engineering, establishing a versatile new platform to simulate novel correlated phenomena based on pseudo Landau levels.

We introduce a framework for emulating graphs and, through them, curved spaces of arbitrary dimension, using arrays of superconducting wires. By discretizing a space into a graph, assigning a superconducting wire with a rigid phase to each vertex, and coupling pairs of wires through Josephson junctions along the graph edges, arbitrary geometries and topologies can be engineered in a controlled setting. The superconducting phases then realize scalar field theories on the emergent geometry. We establish experimentally realistic conditions for implementing these architectures and develop a dictionary relating measurable circuit observables to quantities in the emulated field theory. As an application, we develop the implementation of hyperbolic (Anti-de Sitter) spaces of constant negative curvature and use them as an experimentally accessible platform to explore holographic duality in arbitrary dimensions. We investigate the effects of disorder in the Josephson couplings, which translate into metric variations in the bulk-boundary correspondence, and analyze their impact on boundary scaling exponents both analytically and numerically, finding that holographic duality remains robust even in the presence of strong disorder. Beyond holography, the framework opens a broad range of architectural possibilities, including the exploration of physics on highly nontrivial graphs and toy models of dynamical spacetimes.

We study the relationship between discrete-group topological order, non-Abelian lattice gauge theory, and non-invertible higher-form symmetries in the paradigmatic quantum double model. We analyze how these structures extend away from the fixed-point limit and explore their connection to the confinement of non-Abelian anyons.

The complexity of highly excited eigenstates is a central theme in nonequilibrium many-body physics, underpining questions of thermalization, classical simulability, and quantum information structure. In this work, considering the paradigmatic Rokhsar-Kivelson model, we connect quantum many-body scarring in Abelian lattice gauge theories to an emergent stabilizer structure. We identify a distinct class of scarred eigenstates, termed sublattice scars, originating from gauge-invariant zero modes that form exact stabilizer states. Remarkably, although the underlying Hamiltonian is not a stabilizer Hamiltonian, its eigenspectrum intrinsically hosts exact stabilizer eigenstates. These sublattice scars exhibit vanishing stabilizer R\'enyi entropy together with finite, highly structured entanglement, enabling efficient classical simulation. Exploiting their stabilizer structure, we construct explicit Clifford circuits that prepare these states in a two-dimensional lattice gauge model. Our results demonstrate that the scarred subspace of the Rokhsar-Kivelson spectrum forms an intrinsic stabilizer manifold, revealing a direct connection between stabilizer quantum information, lattice gauge constraints, and quantum many-body scarring.

The chiral magnetic effect (CME) is a fundamental phenomenon in high-energy physics where an electric current is generated along an external magnetic field in the presence of a chirality imbalance, which is a difference between number of left-handed and right-handed fermions. CME is non-equilibrium phenomena that arises as a consequence of the chiral anomaly, which is the breaking of chiral symmetry that introduces a chiral imbalance. In the presence of a finite chiral chemical potential, this im- balance leads to a macroscopic vector current along the magnetic field, defining the CME. CME plays a crucial role in understanding the behavior of relativistic charged fermions and acts a probe for topological charge fluctuations in quantum chromodynamics (QCD) and has significant implications for heavy-ion collisions and early universe cosmology. Despite its broad significance, understanding the real-time dynamics of the CME poses a significant challenge for classical computation due to the sign problem and the exponential complexity of many-body systems. We propose a scheme to simulate the real-time dynamics of the Chiral Magnetic Effect (CME) and chirality-flipping processes using fermions in one-dimensional optical lattices. Our proposal aims to provide a scalable and controllable route to simulate anomaly-induced transport, establishing optical lattices as a promising platform for the real-time study of CME dynamics.

Measurement-induced entanglement transitions (MIETs) represent a new paradigm of nonequilibrium phase transitions, but their existence and universality in some free-fermion systems remain debated. In this thesis, we study both unitary and monitored free-fermion dynamics using analytical and numerical techniques. We analyze the Braid and Gaussian random brickwork circuits. In the Braid circuit, a mapping to a classical model yields an intuitive picture of the entanglement dynamics and allows analytical predictions for the steady-state averages of the entanglement entropy, subsystem purity, and mutual information. In the Gaussian circuit, we adapt methods developed for Haar random circuits to compute the steady-state subsystem purity and numerically show that the annealed average second R´enyi entropy approximates the true R´enyi entropy well in large systems. Including measurements qualitatively changes the dynamics and can lead to entanglement transitions. We map the monitored Braid circuit to a classical model and provide numer- ical evidence that a genuine MIET occurs, and is described by the universality class of the completely packed loop model with crossings. For monitored Hamiltonian models, particle number conservation and a bipartite structure of the model are important for the existence of MIETs. When both symmetries are broken — in our case through adding pairing terms and onsite disorder to a fermionic hopping Hamiltonian — a genuine MIET between a phase with $log(L)^2$ entanglement and an area law phase exists. A numerical analysis of universal quantities supports a description in terms of the $SO(N)$ nonlinear sigma model (NL$\sigma$M) in the replica limit $N \rightarrow 1$. When the particle number is conserved or the bipartite structure is not broken, we find evidence that only finite-size crossovers occur, and the model is in the area law phase for all measurement rates. Finally, we speculate on a classification framework of generic free-fermion models: moni- tored systems are governed by the same NLσMs as their nonunitary circuit counterparts but in the replica limit $N \rightarrow 1$. We discuss how our results and previous literature fit into the framework and begin numerically testing its predictions. A striking conjecture is the existence of exactly one additional generic free-fermion MIET universality class in one dimension.

Non-Abelian topological orders, which support anyonic excitations, are central to quantum computing but remain difficult to realize. We show that the twisted quantum double of the dihedral group—a key family of non-Abelian topological orders—can emerge via Higgsing from a parent O(2) gauge theory. This correspondence is established by matching anyon statistics with Wilson loop observables in a BF theory framework. We further construct lattice models realizing these phases and, through renormalization group analysis, propose that they can undergo a direct transition to a U(1) Coulomb or chiral topological phase at a multicritical point with emergent O(3) symmetry.

I will present an effective gauge field theory of Wigner crystal elasticity, which considers the presence of elastic defects: interstitials/vacancies and dislocations. Using this theory, we calculate defect-defect interaction energies, and study the effects of defect proliferation on the long-wavelength physics of the charged crystal. Unexpectedly, we find that upon a condensation of vacancies or interstitials the corresponding gauge field does not become massive – on the contrary, the number of massless modes in the system increases. We dub this mechanism the anti-Higgs mechanism. [1] P. Matus, "Defects in Wigner crystals: Fracton-elasticity duality and vacancy proliferation", Phys. Rev. B 113 (7), 075138 [2] A. Głódkowski, P. Matus, F. Peña-Benítez, and L. Tsaloukidis, "Quadrupole gauge theory: Anti-Higgs mechanism and elastic dual", Phys. Rev. D 112 (12), L121702

Theoretical analysis of an effective non-Hermitian systems characterized by asymmetric Heisenberg XY interactions in the absence of external magnetic fields demonstrates that maximal bipartite entanglement and quantum phase transitions can be induced exclusively through non-Hermiticity. At thermal equilibrium as $T \rightarrow 0$, the system attains maximal entanglement $C= 1$ for values of the non-Hermiticity parameter greater than a critical value $\gamma > \gamma_c = J(1−\delta^2)^{1/2}$, where $J$ denotes the exchange interaction and $\delta$ represents the anisotropy of the system; conversely, for $$\gamma < \gamma_c $, entanglement is nonmaximal and given by $C= \sqrt{1−(\gamma/J)^2}$. The entanglement undergoes a discontinuous transition to zero precisely at $\gamma =\gamma_c$. This phase transition originates from non-Hermiticity driven ground state degeneracy, which differs fundamentally from an exceptional point. Reference: B . Midya, Non-Hermiticity induced thermal entanglement phase transition, J. Appl. Phys. (2026) (to appear).

We derive an effective field theory (EFT) description for the quantum skyrmion Hall effect (QSkHE) and related topologically non-trivial phases of matter. An almost point-like Landau level with small orbital degeneracy can host an intrinsically 2+1 D topological many-body state, meaning internal degrees of freedom can encode a finite number of spatial dimensions. This almost point-like 2+1 D many-body state plays the role, in the quantum skyrmion Hall effect (QSkHE), that a charged particle plays in the quantum Hall effect. We also present a Matrix formalism for QSkHE, to account for the non-commutative character of gauge theories hosted in LLLs. 1. V. Patil, R. Flores-Calderón, and A. M. Cook, Effective field theory of the quantum skyrmion hall effect (2024), arXiv:2412.19565 [hep-th] 2. V. Patil, A. Banerjee, and A. M. Cook, Microscopic field theories of the quantum skyrmion hall effect (2025), arXiv:2508.16547 [hep-th].

We study the behavior of superfluids defined over a non-commutative (fuzzy) compact space. In particular, we investigate the Bose--Einstein condensation (BEC) and thermal fluctuations of the superfluid density on the surface of a fuzzy sphere. A central feature of these systems is the truncation of the spectrum due to an angular momentum cutoff set by the non-commutativity scale. In ideal and weakly interacting Bose gases, we derive the critical temperature for condensation $T_{BEC}$ and show that, while the compactness of the system facilitates BEC in $d=2$, increasing non-commutativity lowers the critical temperature $T_{BEC}$, ultimately leading to a complete suppression of condensation for high enough degree of non-commutativity. Since superfluidity can occur even in the absence of a condensate, we further investigate superfluid behavior on the fuzzy sphere by deriving the superfluid density from the response to a phase twist (analogous to a Galilei boost) as a function of both the sphere radius and the space non-commutativity parameter.

The fuzzy-sphere regularization has recently emerged as a promising framework for studying conformal criticality in strongly interacting quantum field theories, showing remarkable agreement with the state-operator correspondence in the 3D Ising universality class even at modest system sizes [1]. Building on our recent sign-problem-free formulation of quantum many-body models on the fuzzy sphere and its application to Sp(N) nonlinear sigma models related to deconfined quantum criticality [2,3], we develop a scalable Hybrid Monte Carlo (HMC) approach that enables simulations at substantially larger system sizes. Focusing on the SO(5)-symmetric deconfined quantum critical point from a low-energy field-theory perspective, we investigate the long-standing question of whether the transition is ultimately first or second order. In contrast to conventional microscopic lattice realizations, the fuzzy-sphere formulation provides direct access to the infrared conformal dynamics and excitation spectrum. Our results demonstrate that HMC on the fuzzy sphere is a powerful and efficient nonperturbative framework for exploring conformal fixed points and strongly coupled critical phenomena with many degrees of freedom. [1] Phys. Rev. X 13, 021009 (2023) [2] SciPost Phys. Core 7, 028 (2024) [3] arXiv:2602.11255 (2026)

We propose an S-matrix approach to numerical simulations of network models, applying it to random networks (GKNS networks) previously introduced for the Integer quantum Hall effect (IQHE) plateau transitions, which capture the physics of electrons moving in a strong magnetic field and smooth disorder potential more accurately. The S-matrix method offers significant advantages over the transfer matrix approach, allowing for a high precision calculation of the a localization length critical exponent, $\nu \approx 2.37$. This value aligns closely with the experimental result $\nu_{exp} \approx 2.38$ observed at the IQH transition, while differing notably from the CC model’s value of $\nu_{CC}\approx 2.6$. Additionally, we analyze the applicability of the Harris criterion to the GKNS network disorder and demonstrate that the fluctuations in the geometry are relevant despite the condition $d\nu > 2$, suggesting a need for modification of Harris criterion. Specifically, we find that the fluctuations of the critical point in different quenched configurations of disordered network blocks are of order $L^0$, rather than decreasing as $L^{-d/2}$ as implied by the Harris criterion. This behavior suggests that the GKNS network disorder is never irrelevant, with the critical indices of the system being subject to change. Moreover, we show that the GKNS disordered network differs fundamentally from the usually studied Voronoi-Delaunay and dynamically triangulated random lattices, as the probability of higher connectivity in the GKNS network decaying as a power law rather than exponentially, indicating that the network is "scale-free", which are almost not studied in the context of matter physics.

The spin-$1/2$ $J_1-J_2$-Heisenberg antiferromagnet on the square lattice is a paradigmatic system in quantum magnetism. While a Néel-ordered phase at small $J_2/J_1$ and a stripe-ordered phase at large $J_2/J_1$ are well established, the nature of the intermediate phase remains under debate. Numerical studies have reported conflicting results, proposing either a valence-bond solid phase or a possible $Z_2$ quantum spin liquid. In this work, we study the stability of a candidate $Z_2$ quantum spin liquid phase in this model using a fully self-consistent analytic approach. We first determine the mean-field parametrization of the system self-consistently and then incorporate fluctuation effects beyond mean field theory through an infinite resummation of interaction diagrams within the random phase approximation (RPA). Within the RPA, a collective low energy excitation emerges that allows us to assess the stability of the spin liquid state. At transitions toward magnetically ordered phases, this mode condenses at the corresponding ordering wavevector, whereas it remains gapped within the spin liquid regime. This approach further enables the calculation of the full finite-frequency spectral function, allowing for direct comparison with numerical methods such as variational Monte Carlo and density matrix renormalization group calculations, as well as experimental probes including inelastic neutron scattering.

The merger of two highly entangled systems offers a holographic perspective on the unification of black hole spacetimes. In this ongoing work, we investigate the time evolution of two complex Sachdev-Ye-Kitaev (SYK) models coupled through random four-body interactions. By treating the inter-system coupling as a probabilistic network, we explore the transition from decoupled systems to a single merged entity. Our preliminary analysis reveals a multi-stage thermalization process. We observe that standard spatial entanglement metrics, such as logarithmic negativity and mutual information, saturate rapidly, suggesting an early formation of a geometric bridge. To capture the subsequent scrambling within the newly formed interior, we utilize Entanglement Imagitivity, a measure of timelike correlations. Our early results suggest that Imagitivity continues to grow and exhibits non-monotonic behavior long after spatial metrics plateau, highlighting a prolonged period of internal complexity growth. This study aims to clarify the distinction between the establishment of a geometric connection and the full dynamical unification of quantum spacetimes.

The Eigenstate Thermalization Hypothesis typically governs the relaxation of generic quantum many-body systems. However, systems constructed from competing integrable structures may exhibit anomalous thermalization dynamics. We are currently investigating a one-dimensional spin-1/2 model where an anisotropic Heisenberg interaction competes with a chiral three-spin interaction. By tuning the relative strength between these non-commuting integrable terms, the system undergoes a crossover into an intermediate chaotic regime. While initial spectral analyses show strong level repulsion characteristic of quantum chaos, we observe that the average eigenstate entanglement entropy remains significantly suppressed compared to the ergodic prediction for random pure states. Our ongoing research explores the Liouvillian spectrum of this system to identify the mechanism behind this suppressed thermalization. Current data points to the presence of quasi-conserved operators that create a dynamical bottleneck, effectively fragmenting the phase space and decoupling spectral chaos from full eigenstate ergodicity. These preliminary findings highlight the complex landscape of intermediate dynamical regimes between integrability and chaos.

In this talk, I will introduce fractonic ``superfluids'', which is a type of exotic symmetry-breaking phases where charge-symmetry-breaking is constrained by the presence of higher moment conservation, e.g., dipole moments. The latter originally arises from the field of fracton physics where mobility restriction is considered a vital step towards robust quantum memory. I will unfold a trilogy of the theory of fractonic superfluids by focusing on effective field theory, generalized Mermin-Wagner theorems, the critical dimensions for establishing ODLRO, the construction of generalized vortices and the associated Kosterlitz-Thouless transitions. I will also introduce the construction of generalized bose-Hubbard model on a lattice. Several future questions are proposed and discussed. [References: ArXiv: 1911.02876, 2010.03261, 2412.10280.]

Strong correlation, when combined with dissipation in open systems, can lead to a variety of exotic quantum phenomena. Here, we study nontrivial interplays between non-Fermi liquid behaviors emerging from strong correlation and non-Hermiticity arising from open systems. We propose a practical physical setup that realizes a non-Hermitian multichannel Kondo model. We identify a weak-coupling local moment fixed point and a strong-coupling non-Fermi liquid fixed point under PT symmetry, both are enriched by the non-Hermitian effect. Remarkably, universal unconventional Kondo conductance behaviors are found for both cases, which are distinct from all previously studied Kondo systems. Particularly, we show that an anomalous upturn of conductance could take place with increasing the temperature, originating from the interplay between non-Fermi liquid and non-Hermiticity. Our results identify a novel class of transport phenomena unrecognized before, driven by intertwined effects of correlation and dissipation

Quantum many-body scars break ergodicity and evade thermalization, resulting in area law entanglement entropy even with high energy density. While their quantum correlations and entanglement have been elaborated previously, their capacity in storing extractable energy, quantified by the notion ergotropy, remains an open question. Here we focus on the representative PXP model, and unveil the extensive ergotropy scaling of a family of states interpolating between quantum many-body scars and thermal states, the latter of which are known to be passive with vanishing ergotropy. A phenomenological relation between ergotropy and entanglement is uncovered, which generalizes the existing free fermion integrable results to an interacting scenario. The ergotropy in a dynamical protocol shows that a reset with a global uniform coherent rotation can inject extractable energy, as a proof of principle way to charge a quantum "battery". Our protocol is tailored for near term Rydberg neutral atoms array, while also being feasible for other quantum processors. Our results establish that quantum many-body scars, despite the tiny fraction of the Hilbert space they occupy, can be efficiently exploited for storing extractable energy, and "scarring" a many-body system as a promising route for engineering quantum many-body battery.