arXiv subjects

Abhishodh Prakash

Publications and source records attributed to Abhishodh Prakash.

At least 19 recordsLinked to original sources

arXiv2026

Statistical mechanics of classical fractons on a line

We study the equilibrium statistical mechanics of one-dimensional classical Machian fractons: particles whose dynamics conserves a global dipole moment and whose Hamiltonian couples momentum differences through a position-dependent pair-inertia kernel. Compactly supported interaction kernels have a divergence in the Gibbs partition function, and have been shown to break ergodicity and symmetry by forming non-equilibrium steady states with particle clusters, evading the Hohenberg-Mermin-Wagner-Coleman theorem. In this paper, we consider kernels with non-compact support and study their ergodic properties. For exponentially decaying kernels, graph-Laplacian and matrix-tree bounds provide an extensive free energy suggesting that a putative statistical mechanical description is valid. Similarly, uniform non-local kernels have a super-extensive free energy and require a Kac rescaling. A generalized Hohenberg--Mermin--Wagner--Coleman argument, supported by finite-size scaling, implies symmetry-breaking density order parameter vanishes at all wave vectors melting the long-range translation-breaking density order of compact kernels. To study the resulting equilibrium ensemble, we construct a nonreversible event-chain Monte Carlo (ECMC) algorithm that samples the coupled position-momentum phase space while preserving the dipole moment and total momentum. The ECMC sampling is shown to quantitatively match long time-averaged quantites in Hamiltonian dynamics. The equilibrium liquid exhibits preferred short-range clustering and strongly non-Gaussian single-particle momentum tails associated with the correlated nature of positions and momenta. This paper provides a detailed investigation into the equilibrium liquid properties of the non-compact regime, whilst the companion paper investigates the mechanisms that relax the liquid.

cond-mat.stat-mech↗

arXiv2026

Interface phases and dynamics in two-dimensional quantum magnets: A "holographic" approach from universality to quantum simulation

We introduce a framework to classify quantum phases, phase transitions, and non-equilibrium dynamics of interfaces separating ordered bulk domains in 2D quantum magnets - equivalently, confining strings in dual lattice gauge theories - based on effective 1D Hamiltonians governing geometric fluctuations. Building on a "holographic" approach from [Phys. Rev. Lett. 129, 120601 (2022)], here reinterpreted as an exact bosonization, we uncover a rich quantum phase structure, with a variety of stiff and rough interface phases described by gapped and gapless 1D ground states, respectively, all distinguishable through the statistics of 2D wave-function snapshots. Our framework allows us to predict distinct spatiotemporal scaling laws for non-equilibrium curvature-driven interface dynamics across parameter space, which can be readily probed in existing experiments. We finally show that our approach enables the unprecedented experimental opportunity of directly measuring charge full counting statistics and symmetry-resolved properties of an encoded 1D system, as we explicitly demonstrate by numerically simulating a neutral-atom array experiment.

cond-mat.stat-mech↗

arXiv2026

Classical fractons with cosmological fixed points

Classical fractons are Hamiltonian systems that can develop attractors after projection onto configuration or shape variables, although the full phase space admits none. We study a scale-invariant, dipole-conserving two-parameter family of fracton Hamiltonians $H_{α,β}$. By separating coordinates into scale and shape, we obtain autonomous shape dynamics that admit fixed points which leave a purely scale evolution of the form $R(t)\propto |t|^{α/(α-β)}$. The shape fixed points, which determine the distribution of the expanding particles, are central configurations of power-law Riesz potentials. The distinguished model $(α,β)=(-2,1)$ is unique: its scale evolution takes the Einstein-de Sitter form $R(t)\propto |t|^{2/3}$, its fixed-point equation is the equal-mass Newtonian central-configuration, its large-$N$ distribution is a homogeneous ball, and its homothetic trajectories admit a zero-energy Newtonian gravitational dual. The fixed points are locally stable, and simulations at moderate $N$ approach them from random initial data. Large $N$ simulations reveal a richer class of fixed-points: bound clusters of approximately fixed physical size retain internal motion, while their centers approach unequal-mass Newtonian central configurations and preserve large-scale homogeneity. A scale-separation conjecture yields an effective unequal-mass fracton dynamics for the centers and a corresponding zero-energy Newtonian gravitational dual. Trajectories generically exhibit a bidirectional arrow of time: scale and shape complexity grow away from a Janus point, while Boltzmann entropy grows logarithmically. Together, these features reproduce the salient structure of a flat matter-dominated cosmology. In the distinguished fracton model, all these cosmological analogues emerge as attractor properties, making it a toy model for cosmological dynamics without fine-tuning.

cond-mat.stat-mech↗

arXiv2026

Continuum Fractons: Quantization and the Few Body Problem

We formulate a continuum quantum mechanics for non-relativistic, dipole-conserving fractons. Imposing symmetries and locality results in novel phenomena absent in ordinary quantum mechanical systems. A single fracton has a vanishing Hamiltonian, and thus its spectrum is entirely composed of zero modes. For the two-body problem, the Hamiltonian is perfectly described by Sturm--Liouville (SL) theory. The effective two-body Hamiltonian is an SL operator on $(-1,1)$ whose spectral type is set by the edge behavior of the pair inertia function $K(x)\sim \lvert x -x_\mathrm{edge} \rvert^θ$. We identify a sharp transition at $θ=2$: for $θ<2$ the spectrum is discrete and wavepackets reflect from the edges, whereas for $θ>2$ the spectrum is continuous and wavepackets slow down and, dominantly, squeeze into asymptotically narrow regions at the edges. For three particles, the differential operator corresponding to the Hamiltonian is piecewise defined, requiring several `matching conditions' which cannot be analyzed as easily. We proceed with a lattice regularization that preserves dipole conservation, and implicitly selects a particular continuum Hamiltonian that we analyze numerically. We find a spectral transition in the three-body spectrum, and find evidence for quantum analogs of fracton attractors in both eigenstates and in the time evolution of wavepackets. We provide intuition for these results which suggests that the lack of ergodicity of classical continuum fractons will survive their quantization for large systems.

cond-mat.str-el↗

arXiv2026

Topological Phenomena Protected by Diabolical Textures

We present a new class of topological phenomena in inhomogeneous systems arising from the adiabatic spatial embedding of parametrized families of quantum states such as charge pumps and their generalizations. We demonstrate that each topologically distinct class of these "diabolical textures" gives rise to distinct gapped states that are separated by "trap-scaling" critical points. When the texture varies sufficiently rapidly in space, the critical line terminates abruptly, producing an "unnecessary critical" surface. We demonstrate our results using a microscopic model of non-interacting fermions with a spatially embedded Thouless pump. We study its phase diagram comprehensively and establish its stability to arbitrary perturbations, including interactions, in the vicinity of the critical regions. For systems in arbitrary spatial dimensions and global symmetries, we present a framework to systematically classify diabolical textures using Kitaev's $Ω$ spectrum conjecture.

cond-mat.str-el↗

arXiv2026

Textured phase diagrams of featureless insulators

We study phase diagrams of charge-conserving `class A' non-interacting fermions, focusing on the trivial phase in various dimensions. Such phases are usually termed `featureless' to distinguish them from those others with either symmetry-broken or topological order. We show that the presence of non-trivial topological families of states, including charge pumps and their generalizations, results in phase diagrams being endowed with non-trivial topological textures that can be visualized through Berry phases and their higher-dimensional generalizations. We show that for non-interacting fermion systems with translation invariance, these `higher' Berry phases can be computed using integrals of non-abelian Chern-Simons forms of the Berry-Bloch connection over momentum and parameter spaces. Singularities in these textures correspond to gap-closing loci of `diabolical points', which represent the obstruction to contracting topologically non-trivial families of states, and bulk-boundary correspondence results in a locus of robust boundary modes that terminate at the bulk diabolical points. In the presence of finite chemical potential, we argue that the edge modes are generically robust without any need for fine-tuning for two and higher dimensions, whereas in one dimension they are `estranged' in the phase diagram, i.e. appearing at different parameter values for different edges. We demonstrate our results by constructing several microscopic models of non-interacting fermions. We argue stability to interactions and explore proximate phase diagrams by mapping to continuum field theories.

cond-mat.str-el↗

arXiv2026

Phase space fractons

Perhaps the simplest approach to constructing models with sub-dimensional particles or fractons is to require the conservation of dipole or higher multipole moments. We generalize this approach to allow for moments in phase space and classify all possible classical fracton models with phase-space multipole conservation laws. We focus on a new self-dual model that conserves both dipole and quadrupole moments in position and momentum; we analyze its dynamics and find quasi-periodic orbits in phase space that evade ergodic exploration of the full phase space.

cond-mat.stat-mech↗

arXiv2026

Charge pumps, boundary modes, and the necessity of unnecessary criticality

We link the presence of "unnecessary" quantum critical surfaces within a single gapped phase of matter to the non-trivial topology of families of gapped Hamiltonians that encircle the critical surface. We study a specific set of one-dimensional spin models where each such family forms a one-parameter loop in a two-dimensional phase diagram. Foliating the non-critical region by such loops identifies "radial" and "angular" coordinates in the phase diagram that respectively parametrize different families and different members of a single family. We show that each one-parameter family is a generalized Thouless charge pump, all with the same topological index, and hence the gapped phase undergoes one or more nontrivial boundary phase transitions as we vary the angular coordinate in a loop through members of one family. Tuning the radial coordinate generates loci of boundary critical points that terminate at endpoints of the bulk unnecessary critical line within the gapped phase. We discuss broader implications of our results and possible extensions to higher dimensions.

cond-mat.str-el↗

arXiv2025

Two-dimensional $J_1$-$J_2$ clock model: Enhanced symmetries, emergent orders, and Landau-incompatible transitions

We present a comprehensive study on the frustrated $J_1$-$J_2$ classical $q$-state clock model with even $q>4$ on a two-dimensional square lattice, revealing a rich ensemble of phases driven by competing interactions. In the unfrustrated regime ($J_1>2J_2$), the model reproduces the standard clock model phenomenology: a low-temperature $\mathbb{Z}_q$-broken ferromagnet, an intermediate XY-like critical quasi-long-range-ordered (QLRO) phase with emergent $U(1)$ symmetry, and a high-temperature paramagnet. For $J_1<2J_2$, frustration stabilizes five distinct regimes: the disordered paramagnet, a stripe-ordered phase breaking $\mathbb{Z}_q\times\mathbb{Z}_2$ symmetry, two $\mathbb{Z}_2$-broken nematic phases (one with and one without QLRO), and an exotic stripe phase with emergent discrete $\mathbb{Z}_q$ spin degrees of freedom prohibited in the microscopic Hamiltonian. Remarkably, this seemingly forbidden $\mathbb{Z}_q$ order emerges via a relevant operator in the infrared long-wavelength limit, rather than from an irrelevant perturbation, highlighting a non-standard route to emergence. Using large-scale corner transfer matrix renormalization group calculations, complemented by classical Monte Carlo simulations, we map the complete phase diagram and identify Berezinskii-Kosterlitz-Thouless, Ising, first-order, and unconventional Landau-incompatible transitions between different phases. Finally, we propose an effective field-theoretic framework that encompasses these emergent orders and their interwoven transitions.

cond-mat.stat-mech↗

arXiv2025

Universal Freezing Transitions of Dipole-Conserving Chains

We demonstrate the existence of a universal phase diagram of quantum chains with range-$k$ interactions subject to the conservation of a total charge and its dipole moment. These systems exhibit "freezing" transitions between strongly and weakly Hilbert-space-fragmented phases as the charge filling $ν$ is varied. We show that these continuous phase transitions occur at a critical charge filling of $ν_c=(k-2)^{-1}$ independently of the on-site Hilbert space dimension $d$. To this end, we analytically prove that, for any $d$, any state with $ν<ν_c$ hosts a finite density of sites belonging to "blockages", which we define as subregions of the chain across which transport of charge and dipole moment cannot occur. Some blockages arise from sequences of frozen sites, i.e. sites with an unchanging on-site charge, while others do not involve frozen sites at all. We prove that the presence of blockages implies strong fragmentation of typical symmetry sectors into Krylov subspaces, each of which forms an exponentially vanishing fraction of the total sector. By studying the distribution of blockages we analytically characterise how typical states are subdivided into dynamically disconnected local "active bubbles", and prove that typical eigenstates at these charge fillings exhibit area-law entanglement entropy, while there exist rare eigenstates featuring non-area-law scaling. We also numerically show that for $ν>ν_c$ and arbitrary $d$, typical symmetry sectors are weakly fragmented, with their dominant Krylov sectors constituted of states that are free of blockages. We analytically derive some critical exponents characterising the transition and numerically determine the density of blockages at $ν=ν_c$, with clear implications for transport at the critical point. Finally, we investigate the properties of special-case models for which no phase transitions occur.

cond-mat.str-el↗

arXiv2025

Charge pumps, pivot Hamiltonians and symmetry-protected topological phases

Generalised charge pumps are topological obstructions to trivialising loops in the space of symmetric gapped Hamiltonians. We show that given mild conditions on such pumps, the associated loop has high-symmetry points which must be in distinct symmetry-protected topological (SPT) phases. To further elucidate the connection between pumps and SPTs, we focus on closed paths, `pivot loops', defined by two Hamiltonians, where the first is unitarily evolved by the second `pivot' Hamiltonian. While such pivot loops have been studied as entanglers for SPTs, here we explore their connection to pumps. We construct families of pivot loops which pump charge for various symmetry groups, often leading to SPT phases -- including dipole SPTs. Intriguingly, we find examples where non-trivial pumps do not lead to genuine SPTs but still entangle representation-SPTs (RSPTs). We use the anomaly associated to the non-trivial pump to explain the a priori `unnecessary' criticality between these RSPTs. We also find that particularly nice pivot families form circles in Hamiltonian space, which we show is equivalent to the Hamiltonians satisfying the Dolan-Grady relation -- known from the study of integrable models. This additional structure allows us to derive more powerful constraints on the phase diagram. Natural examples of such circular loops arise from pivoting with the Onsager-integrable chiral clock models, containing the aforementioned RSPT example. In fact, we show that these Onsager pivots underlie general group cohomology-based pumps in one spatial dimension. Finally, we recast the above in the language of equivariant families of Hamiltonians and relate the invariants of the pump to the candidate SPTs. We also highlight how certain SPTs arise in cases where the equivariant family is labelled by spaces that are not manifolds.

cond-mat.str-el↗

arXiv2025

Classical Fractons: Local chaos, global broken ergodicity and an arrow of time

We report new results on classical nonrelativistic dipole conserving particles - fractons. These have been previously shown to exhibit "Machian" dynamics where the motion of one particle requires the presence of others in its proximity, such that dynamics produces ergodicity breaking steady states characterized by clusters. In this work, we show that although the global state breaks ergodicity, a limited version of ergodic behavior is retained within the clusters which may or may not be chaotic, depending on the nature of the microscopic Hamiltonian. In certain cases, we show that the dynamics can be mapped to that of a billiards particle in various stadiums. We also show that the many-fracton trajectories characteristically exhibit a central time or "Janus point" and thus a generic nonequilibrium bidirectional arrow of time.

cond-mat.stat-mech↗

arXiv2025

Pivoting through the chiral-clock family

The Onsager algebra, invented to solve the two-dimensional Ising model, can be used to construct conserved charges for a family of integrable $N$-state chiral clock models. We show how it naturally gives rise to a "pivot" procedure for this family of chiral Hamiltonians. These Hamiltonians have an anti-unitary CPT symmetry that when combined with the usual $\mathbb{Z}_N$ clock symmetry gives a non-abelian dihedral symmetry group $D_{2N}$. We show that this symmetry gives rise to symmetry-protected topological (SPT) order in this family for all even $N$, and representation-SPT (RSPT) physics for all odd $N$. The simplest such example is a next-nearest-neighbour chain generalising the spin-1/2 cluster model, an SPT phase of matter. We derive a matrix-product state representation of its fixed-point ground state along with the ensuing entanglement spectrum and symmetry fractionalisation. We analyse a rich phase diagram combining this model with the Onsager-integrable chiral Potts chain, and find trivial, symmetry-breaking and (R)SPT orders, as well as extended gapless regions. For odd $N$, the phase transitions are "unnecessarily" critical from the SPT point of view.

cond-mat.stat-mech↗

arXiv2025

Classical origins of Landau-incompatible transitions

Continuous phase transitions where symmetry is spontaneously broken are ubiquitous in physics and often found between `Landau-compatible' phases where residual symmetries of one phase are a subset of the other. However, continuous `deconfined quantum critical' transitions between Landau-incompatible symmetry-breaking phases are known to exist in certain quantum systems, often with anomalous microscopic symmetries. In this Letter, we investigate the need for such special conditions. We show that Landau-incompatible transitions can be found in a family of well-known classical statistical mechanical models with anomaly-free symmetries, introduced by José, Kadanoff, Kirkpatrick and Nelson (Phys. Rev. B 16, 1217). The models are anisotropic deformations of the classical 2d XY model labelled by a positive integer $Q$. For a range of temperatures, even $Q$ models exhibit two Landau-incompatible partial symmetry-breaking phases and a direct transition between them for $Q \ge 4$. Characteristic features of deconfined quantum criticality, such as enhanced symmetries and melting of charged defects are easily seen in a classical setting. For odd $Q$, and corresponding temperature ranges, two regions of a single partial symmetry-breaking phase appear, split by a stable `unnecessary critical' line. We discuss experimental systems that realize these transitions and present anomaly-free quantum models that also exhibit similar phase diagrams.

cond-mat.stat-mech↗

arXiv2024

Machian fractons, Hamiltonian attractors and non-equilibrium steady states

We study the $N$ fracton problem in classical mechanics, with fractons defined as point particles that conserve multipole moments up to a given order. We find that the nonlinear Machian dynamics of the fractons is characterized by late-time attractors in position-velocity space for all $N$, despite the absence of attractors in phase space dictated by Liouville's theorem. These attractors violate ergodicity and lead to non-equilibrium steady states, which always break translational symmetry, even in spatial dimensions where the Hohenberg-Mermin-Wagner-Coleman theorem for equilibrium systems forbids such breaking. While a full understanding of the many-body nonlinear problem is a formidable and incomplete task, we provide a conceptual understanding of our results using an adiabatic approximation for the late-time trajectories and an analogy with the idea of `order-by-disorder' borrowed from equilibrium statistical mechanics. Altogether, these fracton systems host a new paradigm for Hamiltonian dynamics and non-equilibrium many-body physics.

cond-mat.stat-mech↗

arXiv2024

Symmetry-Enriched Criticality in a Coupled Spin-Ladder

We study a one-dimensional ladder of two coupled XXZ spin chains and identify several distinct gapless symmetry-enriched critical phases. These have the same unbroken symmetries and long-wavelength description, but cannot be connected without encountering either a phase transition or other intermediate phases. Using bosonizaion, we analyze the nature of their distinction by determining how microscopic symmetries are manifested in the long-wavelength fields, the behavior of charged local and nonlocal operators, and identify the universality class of all direct continuous phase transitions between them. One of these phases is a gapless topological phase with protected edge modes. We characterize its precise nature and place it within the broader classification. We also find the occurrence of `multiversality' in the phase diagram, wherein two fixed phases are separated by continuous transitions with different universality classes in different parameter regimes. We determine the phase diagram and all its aspects, as well as verify our predictions numerically using density matrix renormalization group and a mapping onto an effective spin-1 model.

cond-mat.str-el↗

arXiv2024

Classical Non-Relativistic Fractons

We initiate the study of the classical mechanics of non-relativistic fractons in its simplest setting - that of identical one dimensional particles with local Hamiltonians characterized by by a conserved dipole moment in addition to the usual symmetries of space and time translation invariance. We introduce a family of models and study the $N$ body problem for them. We find that locality leads to a ``Machian" dynamics in which a given particle exhibits finite inertia only if within a specified distance of at least another one. For well separated particles this leads to immobility, much as for quantum models of fractons discussed before. For two or more particles within inertial reach of each other at the start of motion we get an interesting interplay of inertia and interactions. Specifically for a solvable ``inertia only" model of fractons we find that $N=2$ particles always become immobile at long times. Remarkably $N =3$ particles generically evolve to a late time state with one immobile particle and two that oscillate about a common center of mass with generalizations of such ``Machian clusters" for $N > 3$ . Interestingly, Machian clusters exhibit physical limit cycles in a Hamiltonian system even though mathematical limit cycles are forbidden by Liouville's theorem.

cond-mat.str-el↗

arXiv2023

Long-ranged spectral correlations in eigenstate phases

We study non-local measures of spectral correlations and their utility in characterizing and distinguishing between the distinct eigenstate phases of quantum chaotic and many-body localized systems. We focus on two related quantities, the spectral form factor and the density of all spectral gaps, and show that they furnish unique signatures that can be used to sharply identify the two phases. We demonstrate this by numerically studying three one-dimensional quantum spin chain models with (i) quenched disorder, (ii) periodic drive (Floquet), and (iii) quasiperiodic detuning. We also clarify in what ways the signatures are universal and in what ways they are not. More generally, this thorough analysis is expected to play a useful role in classifying phases of disorder systems.

cond-mat.dis-nn↗