arXiv subjects

S. L. Sondhi

Publications and source records attributed to S. L. Sondhi.

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

On Rare Nonresonant Regions and Subdiffusive Transport in an Interacting Disordered Quantum Chain

We study rare nonresonant regions in a canonical one-dimensional disordered quantum spin chain by directly implementing the iterated Schrieffer-Wolff construction underlying the recent work of De Roeck, Giacomin, Huveneers and Prosniak on subdiffusive transport. For finite systems, we compute the probability that a disorder realization remains nonresonant through successive scales of the flow, while separately monitoring operator proliferation and the spatial localization of dressed local observables. The survival probability decays at most exponentially with system size over the numerically accessible regime. Resolving this decay scale by scale yields failure rates associated with successive Schrieffer-Wolff steps. The first rate is obtained analytically in excellent agreement with numerics, while higher-scale rates decrease rapidly throughout the regime studied. These results support the summability mechanism required for exponentially rare but parametrically long nonresonant regions, which provide the insulating bottlenecks responsible for subdiffusive transport. At the smallest couplings studied, the survival probability under our conditions exceeds the rigorous lower bound by six to seven orders of magnitude, demonstrating how conservative the constants required by the proof are while confirming that its underlying physical mechanism is quantitatively visible at accessible scales. More broadly, our results show how direct numerical implementations can provide an independent and physically transparent test of technically demanding constructive proofs, a methodology that may become increasingly useful as machine-assisted proofs become more common.

cond-mat.dis-nn↗

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

Running Quantum Computers in Discovery Mode

Using a 36-qubit quantum processor, we demonstrate that, by operating in conjunction with a classical machine learning agent, quantum computers can discover instances of interesting quantum many-body dynamics. The central object in this new mode of use of a quantum device is an "interest function" defined for a given circuit (family) instance that can be evaluated on a quantum computer. The circuit is adapted by the learning agent to maximize interest. We illustrate this approach using two examples and show that, within a sufficiently general circuit family, two simple interest functions based on (i) binary classifiability of evolved states and (ii) spectral properties of the unitary circuit, are maximized by discrete time crystals (DTCs) and dual-unitary circuits, respectively. For the classifiability-based interest function, we implement the protocol on a superconducting quantum processor and find that it indeed discovers DTCs with high probability. For the dual-unitaries, our simulations of the dynamics suggest that an interest-function optimization would have set us close to a discovery of such unitaries. Our results using quantum devices and accompanying simulations suggest that learning agents with access to quantum-computing resources can almost autonomously discover new phenomena in many-body quantum dynamics, and establish the design of good interest functions optimizable in hybrid devices as a paradigm for quantum many-body physics.

quant-ph↗

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

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↗

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↗

arXiv2024

Quantum order by disorder in Frustrated Spin Nanotubes

We investigate quantum order by disorder in a frustrated spin nanotube formed by wrapping a $J_1$-$J_2$ Heisenberg model at 45$^\circ$ around a cylinder. Using Schwinger boson theory and Density Matrix Renormalization Group (DMRG), we have computed the ground-state phase diagram to reveal a $\mathbb{Z}_2$ phase in which collinear spin stripes form a right or left handed helix around the nanotube. We have derived an analytic estimate for the critical $η_c=J_1/2J_2$ of the $\mathbb{Z}_2$ helical phase transition, which is in agreement with the DMRG results. By evaluating the entanglement spectrum and nonlocal string order parameters we discuss the topology of the $\mathbb{Z}_2$-helical phase.

cond-mat.str-el↗

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

Utility of virtual qubits in trapped-ion quantum computers

We propose encoding multiple qubits inside ions in existing trapped-ion quantum computers to access more qubits and to simplify circuits implementing standard algorithms. By using such `virtual' qubits, some inter-ion gates can be replaced by intra-ion gates, reducing the use of vibrational modes of the ion chain, leading to less noise. We discuss specific examples such as the Bernstein-Vazirani algorithm and random circuit sampling, using a small number of virtual qubits. Additionally, virtual qubits enable using larger number of data qubits for an error correcting code, and we consider the repetition code as an example. We also lay out practical considerations to be made when choosing states to encode virtual qubits in $^{137}\mathrm{Ba}^+$ ions, and for preparing states and performing measurements.

quant-ph↗

arXiv2024

Random-matrix models of monitored quantum circuits

We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically, including the purification time and the distribution of Born probabilities. The latter generalizes the Porter-Thomas distribution for random unitary circuits to the monitored setting and is log-normal at long times. We also consider weak measurements that interpolate between identity quantum channels and projective measurements. In this setting, we derive an exactly solvable Fokker-Planck equation for the joint distribution of singular values of Kraus operators, analogous to the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation modelling disordered quantum wires. We expect that the statistical properties of Kraus operators we have established for these simple systems will serve as a model for the entangling phase of monitored quantum systems more generally.

quant-ph↗

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↗

arXiv2024

Entanglement Transitions in Unitary Circuit Games

Repeated projective measurements in unitary circuits can lead to an entanglement phase transition as the measurement rate is tuned. In this work, we consider a different setting in which the projective measurements are replaced by dynamically chosen unitary gates that minimize the entanglement. This can be seen as a one-dimensional unitary circuit game in which two players get to place unitary gates on randomly assigned bonds at different rates: The "entangler" applies a random local unitary gate with the aim of generating extensive (volume law) entanglement. The "disentangler," based on limited knowledge about the state, chooses a unitary gate to reduce the entanglement entropy on the assigned bond with the goal of limiting to only finite (area law) entanglement. In order to elucidate the resulting entanglement dynamics, we consider three different scenarios: (i) a classical discrete height model, (ii) a Clifford circuit, and (iii) a general $U(4)$ unitary circuit. We find that both the classical and Clifford circuit models exhibit phase transitions as a function of the rate that the disentangler places a gate, which have similar properties that can be understood through a connection to the stochastic Fredkin chain. In contrast, the "entangler" always wins when using Haar random unitary gates and we observe extensive, volume law entanglement for all non-zero rates of entangling.

quant-ph↗

arXiv2023

Arresting dynamics in hardcore spin models

We study the dynamics of hardcore spin models on the square and triangular lattice, constructed by analogy to hard spheres, where the translational degrees of freedom of the spheres are replaced by orientational degrees of freedom of spins on a lattice and the packing fraction as a control parameter is replaced by an exclusion angle. In equilibrium, models on both lattices exhibit a Kosterlitz-Thouless transition at an exclusion angle $Δ_{\rm KT}$. We devise compression protocols for hardcore spins and find that {\it any} protocol that changes the exclusion angle nonadiabatically, if endowed with only local dynamics, fails to compress random initial states beyond an angle $Δ_{\rm J}> Δ_{\rm KT}$. This coincides with a doubly algebraic divergence of the relaxation time of compressed states towards equilibrium. We identify a remarkably simple mechanism underpinning this divergent timescale: topological defects involved in the phase ordering kinetics of the system become incompatible with the hardcore spin constraint, leading to a vanishing defect mobility as $Δ\rightarrowΔ_{\rm J}$.

cond-mat.stat-mech↗

arXiv2023

Dynamics and transport in the boundary-driven dissipative Klein-Gordon chain

Motivated by experiments on chains of superconducting qubits, we consider the dynamics of a classical Klein-Gordon chain coupled to coherent driving and subject to dissipation solely at its boundaries. As the strength of the boundary driving is increased, this minimal classical model recovers the main features of the "dissipative phase transition" seen experimentally. Between the transmitting and non-transmitting regimes on either side of this transition (which support ballistic and diffusive energy transport respectively), we observe additional dynamical regimes of interest. These include a regime of superdiffusive energy transport at weaker driving strengths, together with a "resonant nonlinear wave" regime at stronger driving strengths, which is characterized by emergent translation symmetry, ballistic energy transport, and coherent oscillations of a nonlinear normal mode. We propose a non-local Lyapunov exponent as an experimentally measurable diagnostic of many-body chaos in this system, and more generally in open systems that are only coupled to an environment at their boundaries.

cond-mat.stat-mech↗

arXiv2023

A multi-player, multi-team nonlocal game for the toric code

Nonlocal games yield an unusual perspective on entangled quantum states. The defining property of such games is that a set of players in joint possession of an entangled state can win the game with higher probability than is allowed by classical physics. Here we construct a nonlocal game that can be won with certainty by $2N$ players if they have access to the ground state of the toric code on as many qubits. By contrast, the game cannot be won by classical players more than half the time in the large $N$ limit. Our game differs from previous examples because it arranges the players on a lattice and allows them to carry out quantum operations in teams, whose composition is dynamically specified. This is natural when seeking to characterize the degree of quantumness of non-trivial many-body states, which potentially include states in much more varied phases of matter than the toric code. We present generalizations of the toric code game to states with $\mathbb{Z}_M$ topological order.

quant-ph↗

arXiv2023

Playing nonlocal games with phases of quantum matter

The parity game is an example of a nonlocal game: by sharing a Greenberger-Horne-Zeilinger (GHZ) state before playing this game, the players can win with a higher probability than is allowed by classical physics. The GHZ state of $N$ qubits is also the ground state of the ferromagnetic quantum Ising model on $N$ qubits in the limit of vanishingly weak quantum fluctuations. Motivated by this observation, we examine the probability that $N$ players who share the ground state of a generic quantum Ising model, which exhibits non-vanishing quantum fluctuations, still win the parity game using the protocol optimized for the GHZ state. Our main result is a modified parity game for which this protocol asymptotically exhibits quantum advantage in precisely the ferromagnetic phase of the quantum Ising model. We further prove that the ground state of the exactly soluble $d=1+1$ transverse-field Ising model can provide a quantum advantage for the parity game over an even wider region, which includes the entire ferromagnetic phase, the critical point and part of the paramagnetic phase. By contrast, we find examples of topological phases and symmetry-protected topological (SPT) phases of matter, namely the deconfined phase of the toric code Hamiltonian and the $\mathbb{Z}_2 \times \mathbb{Z}_2$ SPT phase in one dimension, that do not exhibit an analogous quantum advantage away from their fixed points.

quant-ph↗

arXiv2022

On Classical and Hybrid Shadows of Quantum States

Classical shadows are a computationally efficient approach to storing quantum states on a classical computer for the purposes of estimating expectation values of local observables, obtained by performing repeated random measurements. In this note we offer some comments on this approach. We note that the resources needed to form classical shadows with bounded relative error depend strongly on the target state. We then comment on the advantages and limitations of using classical shadows to simulate many-body dynamics. In addition, we introduce the notion of a hybrid shadow, constructed from measurements on a part of the system instead of the entirety, which provides a framework to gain more insight into the nature of shadow states as one reduces the size of the subsystem measured, and a potential alternative to compressing quantum states.

quant-ph↗