arXiv subjects

Alexey Khudorozhkov

Publications and source records attributed to Alexey Khudorozhkov.

8 recordsLinked to original sources

arXiv2026

Quantum Fragmentation

We introduce a systematic protocol for constructing quantum Hilbert-space-fragmented Hamiltonians, whose Krylov-sector structure, unlike in classically fragmented models, can be fully resolved only in an entangled basis. The protocol takes as input a classically fragmented model and uses a Rokhsar-Kivelson type construction to promote it to a quantum fragmented model. Notably, the procedure also works with non-fragmented inputs (such as Ising models). We explain how the Krylov sectors of the resulting quantum fragmented model may be labeled and counted in one dimension, and outline experimentally accessible verification of quantum fragmentation, assuming the ability to prepare specific initial states and perform tomography on reduced density matrices. We further analyze the entanglement structure of the entangled basis underlying quantum fragmentation, which sharply distinguishes it from both classical fragmentation and the trivial "fragmentation" of generic Hamiltonians in their eigenbasis. We also extend the construction to higher dimensions, with an explicit proof of principle example in two dimensions. We expect these results to open a new route to the systematic exploration of quantum fragmentation.

quant-ph↗

arXiv2025

Observation of an anomaly in the statistics of Kibble-Zurek defects

The Kibble-Zurek mechanism quantifies defect formation during adiabatic passage across a continuous phase transition, providing key insights into universality in quantum many-body systems. We explore counting statistics of defects in adiabatic passage experiments on long 1D Rydberg atom chains. The experiments reveal an anomaly in the defect number distribution at long ramp times, challenging the hypothesis of defect formation through independent domain mergers. Numerical simulations confirm the anomaly and suggest its link to non-critical coarsening dynamics, which we suppress in prepare-and-hold experiments. Our results highlight the ability of quantum simulators to uncover unexpected correlated quantum phenomena.

quant-ph↗

arXiv2025

Strong Hilbert space fragmentation and fractons from subsystem and higher-form symmetries

We introduce a new route to Hilbert space fragmentation in high dimensions leveraging the group-word formalism. We show that taking strongly fragmented models in one dimension and "lifting" to higher dimensions using subsystem symmetries can yield strongly fragmented dynamics in higher dimensions, with subdimensional (e.g., lineonic) excitations. This provides a new route to higher-dimensional strong fragmentation, and also a new route to fractonic behavior. Meanwhile, lifting one-dimensional strongly fragmented models to higher dimensions using higher-form symmetries yields models with topologically robust weak fragmentation. In three or more spatial dimensions, one can also "mix and match" subsystem and higher-form symmetries, leading to canonical fracton models such as X-cube. We speculate that this approach could also yield a new route to non-Abelian fractons. These constructions unify a number of phenomena that have been discussed in the literature, as well as furnishing models with novel properties.

cond-mat.stat-mech↗

arXiv2025

Probing emergent prethermal dynamics and resonant melting on a programmable quantum simulator

The dynamics of isolated quantum systems following a sudden quench plays a central role in many areas of material science, high-energy physics, and quantum chemistry. Featuring complex phenomena with implications for thermalization, non-equilibrium phase transitions, and Floquet phase engineering, such far-from-equilibrium quantum dynamics is challenging to study numerically, in particular, in high-dimensional systems. Here, we use a programmable neutral atom quantum simulator to systematically explore quench dynamics in spin models with up to 180 qubits. By initializing the system in a product state and performing quenches across a broad parameter space, we discover several stable, qualitatively distinct dynamical regimes. We trace their robustness to Floquet-like prethermal steady states that are stabilized over long emergent timescales by strong dynamical constraints. In addition, we observe sharp peaks in the dynamical response that are quantitatively explained by the structured melting of prethermalization through resonances. In two dimensions, we uncover a sharp dynamical response change that converges with increased system size, that is linked to the proliferation of Néel-order defects and indicative of a dynamical phase transition with no equilibrium analogs. Uncovering an intricate interplay between quantum prethermalization and emergent dynamical phases, our results demonstrate the use of quantum simulators for revealing complex non-equilibrium quantum many-body phenomena.

quant-ph↗

arXiv2025

Robust Hilbert space fragmentation in group-valued loop models

We introduce a large class of models exhibiting robust ergodicity breaking in quantum dynamics. Our work is inspired by recent discussions of "topologically robust Hilbert space fragmentation," but massively generalizes in two directions: firstly from states describable as "loop-soups" to a broader class of states reminiscent of string-nets and sponges, and secondly from models restricted to square or cubic lattices, to models defined on arbitrary lattices (and even arbitrary graphs without translation invariance). Our constructions leverage a recently proposed group-theory framework [PRX 14, 021034 (2024)], and identify a host of new phenomena arising from the interplay of "group-model dynamics" and lattice structure. We make crisp connections to gauge theories, and our construction generalizes Kitaev's quantum double to infinite groups.

cond-mat.stat-mech↗

arXiv2024

Glassy word problems: ultraslow relaxation, Hilbert space jamming, and computational complexity

We introduce a family of local models of dynamics based on ``word problems'' from computer science and group theory, for which we can place rigorous lower bounds on relaxation timescales. These models can be regarded either as random circuit or local Hamiltonian dynamics, and include many familiar examples of constrained dynamics as special cases. The configuration space of these models splits into dynamically disconnected sectors, and for initial states to relax, they must ``work out'' the other states in the sector to which they belong. When this problem has a high time complexity, relaxation is slow. In some of the cases we study, this problem also has high space complexity. When the space complexity is larger than the system size, an unconventional type of jamming transition can occur, whereby a system of a fixed size is not ergodic, but can be made ergodic by appending a large reservoir of sites in a trivial product state. This manifests itself in a new type of Hilbert space fragmentation that we call fragile fragmentation. We present explicit examples where slow relaxation and jamming strongly modify the hydrodynamics of conserved densities. In one example, density modulations of wavevector $q$ exhibit almost no relaxation until times $O(\exp(1/q))$, at which point they abruptly collapse. We also comment on extensions of our results to higher dimensions.

quant-ph↗

arXiv2023

$U(1)$ symmetry-enriched toric code

We propose and study a generalization of Kitaev's $\mathbb Z_2$ toric code on a square lattice with an additional global $U(1)$ symmetry. Using Quantum Monte Carlo simulation, we find strong evidence for a topologically ordered ground state manifold with indications of UV/IR mixing, i.e., the topological degeneracy of the ground state depends on the microscopic details of the lattice. Specifically, the ground state degeneracy depends on the lattice tilt relative to the directions of the torus cycles. In particular, we observe that while the usual compactification along the vertical/horizontal lines of the square lattice shows a two-fold ground state degeneracy, compactifying the lattice at $45^\circ$ leads to a three-fold degeneracy. In addition to its unusual topological properties, this system also exhibits Hilbert space fragmentation. Finally, we propose a candidate experimental realization of the model in an array of superconducting quantum wires.

cond-mat.str-el↗

arXiv2022

Hilbert space fragmentation in a 2D quantum spin system with subsystem symmetries

We consider a 2D quantum spin model with ring-exchange interaction that has subsystem symmetries associated to conserved magnetization along rows and columns of a square lattice, which implies the conservation of the global dipole moment. In a certain regime, the model is non-integrable, but violates the eigenstate thermalization hypothesis through an extensive Hilbert space fragmentation, including an exponential number of inert subsectors with trivial dynamics, arising from kinetic constraints. While subsystem symmetries are quite restrictive for the dynamics, we show that they alone cannot account for such a number of inert states, even with infinite-range interactions. We present a procedure for constructing shielding structures that can separate and disentangle dynamically active regions from each other. Notably, subsystem symmetries allow the thickness of the shields to be dependent only on the interaction range rather than on the size of the active regions, unlike in the case of generic dipole-conserving systems.

cond-mat.str-el↗