arXiv subjects

Sthitadhi Roy

Publications and source records attributed to Sthitadhi Roy.

At least 19 recordsLinked to original sources

arXiv2026

Dynamics of local quantum information in random unitary circuits

The physics of information scrambling in quantum many-body systems is intimately related to thermalisation and emergence of chaos. However, its standard characterisation through bipartite entanglement or operator growth remains inherently coarse-grained, obscuring the spatiotemporal anatomy of how quantum information flows between different regions of the system and across various length scales. In this work, we develop a theory for the dynamics of local information in local random unitary circuits which resolves the fine-grained microscopic structures of local information flow in such systems. Using the framework of information lattice which systematises the information content at each length scale within each subsystem, we identify a distribution of length scales at which information resides and obtain the dynamics of the distribution. For Haar-random circuits with infinite local Hilbert-space dimensions, we map this dynamics onto an exact classical stochastic process which reveals that this distribution is described by a Tracy-Widom form which moves ballistically in time ($ \propto t$) toward larger scales, accompanied by a $\sim t^{1/3}$ broadening. We also find the same qualitative behaviour for random Clifford circuits acting on qubits. The similar scaling behaviour in two rather different settings hints strongly towards the universality of our results. In the case of Clifford circuits, we develop a phenomenological Markov process for the dynamics of the stabiliser generators in a specific gauge which confirms the Tracy-Widom distribution and the $t^{1/3}$ scaling of the fluctuations. Ultimately, our results establish the universal properties of the dynamics of local quantum information in a length scale-resolved fashion and provide a possible route towards bridging exact microscopic theories for information dynamics with emergent hydrodynamic descriptions of information flow.

quant-ph↗

arXiv2026

Quantum Chaos and Diffusive Transport from Geometric Randomness

The physics of quantum chaos and diffusive transport is typically studied in settings with microscopic disorder or many-body interactions. In this Letter, we demonstrate that these phenomena can arise purely from geometric randomness. By studying non-interacting quantum particles on random locally tree-like layered graphs with uniform couplings, we show that the geometric randomness and effective graph dimensionality dictates the presence of chaotic dynamics or lack thereof. These graphs can be considered as structurally disordered generalisations of regular square lattices or ladders, or equivalently as multi-component one-dimensional chains with random links between the components. We find that an extensive layer size yields robust quantum chaos, level repulsion, and diffusive transport. Conversely, in the quasi-one-dimensional limit, we find the coexistence of extensive number of localised and delocalised states -- this leads to suppressed level repulsion accompanied by the latter driving ballistic transport. These results establish geometric randomness as a fundamental and independent mechanism for generating and tuning quantum chaos.

cond-mat.stat-mech↗

arXiv2026

Locality of deep thermalisation through the lens of entanglement teleportation

Deep thermalisation characterises the emergence of universal quantum state ensembles on subsystems due to projective measurements on their complement. We study the notion of locality, or lack thereof, in this phenomenon by considering a subsystem partitioned into two disjoint subregions which remain causally disconnected at all times under unitary dynamics. We show that the onset of deep thermalisation in this geometry is fundamentally bounded by measurement-induced entanglement teleportation between the subregions. While measurements on the environment generate entanglement across the disconnected partitions -- suggesting an apparent non-locality -- we demonstrate that generic locally interacting systems exhibit an emergent locality. Specifically, the timescales for both deep thermalisation and entanglement teleportation scale logarithmically with the distance separating the subregions. Exceptions to this include special circuits where the randomness of the measurement outcomes is perfectly transmitted to the ensemble of states of the subsystem, conditioned on the outcomes; in such cases the timescale for deep thermalisation is finite leading to genuine non-locality.

quant-ph↗

arXiv2026

On the emergence of quantum many-body chaos for tunably-broken integrability

We develop a quantitative theory for the emergence of quantum many-body chaos as integrability is broken via a tunable parameter. In a circuit model of free fermions, 'doped' with a tunable density of integrability-breaking gates, we uncover the microscopic mechanisms underpinning the crossover from early-time integrable behaviour to late-time chaos through the lens of the out-of-time-ordered correlators (OTOCs). The integrability-breaking gates act as local, in spacetime, hotspots which locally amplify the OTOCs such that an accumulation of them eventually leads to fully-developed chaos. We identify the explicit characteristic time and length scales governing this crossover, as well as the dependence of the chaotic OTOC characteristics -- such as the butterfly velocity and front broadening -- on the integrability-breaking parameter.

cond-mat.stat-mech↗

arXiv2026

Robust Correlation-Induced Localization Under Time-Reversal Symmetry Breaking

We study Anderson localization in a one-dimensional disordered system with long-range correlated hopping decaying as $1/r^{a}$ with complex hopping amplitudes that break time-reversal symmetry in a tunable fashion by varying their argument. We find analytically a corelation-induced algebraic localization that is robust to a finite strength of the time-reversal-symmetry-breaking parameter, beyond which all states delocalize. This establishes a localization--delocalization transition driven by the interplay between long-ranged correlated hopping and time-reversal symmetry breaking. In addition to obtaining the static localization phase diagram, we also investigate the dynamical phase diagram through the lens of wavepacket spreading. We find that the growth in time of the mean-squared displacement of a wavepacket, which is subdiffusive for the time-reversal symmetric case, becomes diffusive for any finite value of the time-reversal-symmetry-breaking parameter.

cond-mat.dis-nn↗

arXiv2026

Krylov-space anatomy and spread complexity of a disordered quantum spin chain

We investigate the anatomy and complexity of quantum states in Krylov space, in the ergodic and many-body localised (MBL) phases of a disordered, interacting spin chain. The Krylov basis generated by the Hamiltonian from an initial state provides a representation in which the spread of the time-evolving state constitutes a basis-optimised measure of complexity. We show that the long-time Krylov spread complexity sharply distinguishes the two phases. In the ergodic regime, the infinite-time complexity scales linearly with the Fock-space dimension, indicating that the state spreads over a finite fraction of the Krylov chain. By contrast, it grows sublinearly in the MBL regime, implying that the long-time state occupies only a vanishing fraction of the chain. Further, the profile of the infinite-time state along the Krylov chain exhibits a stretched-exponential decay in the MBL regime. This behaviour reflects a broad distribution of decay lengthscales, associated with different eigenstates contributing to the long-time state. Consistently, a large-deviation analysis of the statistics of eigenstate spread complexities shows that while the ergodic regime receives contributions from almost all eigenstates, the complexity in the MBL regime is dominated by a vanishing fraction of eigenstates, which have anomalously large complexity relative to the typical ones.

cond-mat.dis-nn↗

arXiv2026

The damage spreading transition: a hierarchy of renormalization group fixed points

Deterministic classical cellular automata can be in two phases, depending on how irreversible the dynamical rules are. In the strongly irreversible phase, trajectories with different initial conditions coalesce quickly, while in the weakly irreversible phase, trajectories with different initial conditions can remain different for a time exponential in the system volume. The transition between these phases is referred to as the damage-spreading transition (the "damaged" sites are those that differ between the trajectories). We develop a theory for this transition. In the simplest and most generic setting, the transition is known to be related to directed percolation, one of the best-studied nonequilibrium phase transitions. However, we show that full theory of the damage-spreading critical point is richer than directed percolation, and contains an infinite hierarchy of sectors of local observables. Directed percolation describes the first level of the hierarchy. The higher observables include "overlaps" for multiple trajectories, and may be labeled by set partitions. (These higher observables arise naturally if, for example, we consider decay of entropy under the irreversible dynamics.) The full hierarchy yields a hierarchy of nonequilibrium fixed points for reaction-diffusion-type processes, all of which contain directed percolation as a subsector, but which possess additional universal critical exponents. We analyze these higher fixed points using a field theory formulation and renormalization group arguments, and using simulations in 1+1 dimensions.

cond-mat.stat-mech↗

arXiv2026

Arrested Relaxation in a Disorder-Free Coulomb Spin Liquid

We investigate Coulomb spin liquids in classical spin-3/2 ice and show that the enlarged on-site Hilbert space gives rise to a qualitatively new class of such phases. Beyond the conventional magnetic monopoles of spin-1/2 ice, the system hosts additional low-energy crystal-field excitations, whose interplay with monopoles significantly modifies both equilibrium and non-equilibrium properties. Following a thermal quench, we find a pronounced dynamical arrest manifested in an exponentially long-lived {athermal} plateau in spin autocorrelations. This constitutes a rare example of dynamical arrest in a short-range interacting, disorder-free system. We demonstrate that the arrested dynamics originate from novel composite excitation structures unique to spin-3/2 ice and from kinetically constrained relaxation pathways that require activated processes. Our results establish higher-spin ice as a fertile platform for realising unconventional Coulomb spin liquids and dynamical arrest without quenched disorder.

cond-mat.str-el↗

arXiv2026

How many-body chaos emerges in the presence of quasiparticles

Many-body chaos is a default property of many-body systems; at the same time, near-integrable behaviour due to weakly interacting quasiparticles is ubiquitous throughout condensed matter at low temperature. There must therefore be a, possibly generic, crossover between these very different regimes. Here, we develop a theory encapsulating the notion of a cascade of lightcones seeded by sequences of scattering of weakly interacting harmonic modes as witnessed by a suitably defined chaos diagnostic (classical decorrelator) that measures the spatiotemporal profile of many-body chaos. Our numerics deals with the concrete case of a classical Heisenberg chain, for either sign of the interaction, at low temperatures where the short-time dynamics are well captured in terms of non-interacting spin waves. To model low-temperature dynamics, we use ensembles of initial states with randomly embedded point defects in an otherwise ordered background, which provides a controlled setting for studying the scattering events. The decorrelator exhibits a short-time integrable regime followed by an intermediate `scarred' regime of the cascade of lightcones in progress; these then overlap, leading to an avalanche of scattering events which finally yields the standard long-time signature of many-body chaos.

cond-mat.stat-mech↗

arXiv2026

Anderson localisation in spatially structured random graphs

We study Anderson localisation on high-dimensional graphs with spatial structure induced by long-ranged but distance-dependent hopping. To this end, we introduce a class of models that interpolate between the short-range Anderson model on a random regular graph and fully connected models with statistically uniform hopping, by embedding a random regular graph into a complete graph and allowing hopping amplitudes to decay exponentially with graph distance. The competition between the exponentially growing number of neighbours with graph distance and the exponentially decaying hopping amplitude positions our models effectively as power-law hopping generalisation of the Anderson model on random regular graphs. Using a combination of numerical exact diagonalisation and analytical renormalised perturbation theory, we establish the resulting localisation phase diagram emerging from the interplay of the lengthscale associated to the hopping range and the onsite disorder strength. We find that increasing the hopping range shifts the localisation transition to stronger disorder, and that beyond a critical range the localised phase ceases to exist even at arbitrarily strong disorder. Our results indicate a direct Anderson transition between delocalised and localised phases, with no evidence for an intervening multifractal phase, for both deterministic and random hopping models. A scaling analysis based on inverse participation ratios reveals behaviour consistent with a Kosterlitz-Thouless-like transition with two-parameter scaling, in line with Anderson transitions on high-dimensional graphs. We also observe distinct critical behaviour in average and typical correlation functions, reflecting the different scaling properties of generalised inverse participation ratios.

cond-mat.dis-nn↗

arXiv2025

Information phases of partial projected ensembles generated from random quantum states and scrambling dynamics

The projected ensemble -- an ensemble of pure states on a subsystem conditioned on projective measurement outcomes on its complement -- provides a finer probe of ergodicity and information structure than the reduced density matrix of the subsystem in bipartite quantum states. This framework can be generalised to partial projected ensembles in tripartite settings, where outcomes from part of the measured subsystem are discarded, leading to ensembles of mixed states. We show that information measures defined for such ensembles, in particular the Holevo information, yield a more detailed characterisation of how quantum information is distributed between subsystems compared to conventional entanglement measures. Using exact analytical results supported by numerical results, we uncover a qualitative change in the scaling of the Holevo information with system size in partial projected ensembles generated by Haar-random states, as the relative sizes of the subsystem are varied. In one phase, the Holevo information decays exponentially with system size, while in the other it grows linearly, thereby defining distinct information phases separated by sharp transitions signalled by non-analyticities in the Holevo information. The exponentially decaying phase rigorously establishes the existence of a measurement-invisible quantum-correlated phase -- a manifestation of many-body information scrambling with no bipartite analogue. We contrast this information-phase diagram with the entanglement-phase structure of tripartite Haar-random states obtained from logarithmic negativity, and show that the Holevo information reveals additional fine structure beyond conventional entanglement measures. Finally, we show that these information phases, as characterised by the Holevo information, emerge in the dynamics of chaotic quantum circuits and discuss the associated timescales.

quant-ph↗

arXiv2025

Multifractality in high-dimensional graphs induced by correlated radial disorder

We introduce a class of models containing robust and analytically demonstrable multifractality induced by disorder correlations. Specifically, we investigate the statistics of eigenstates of disordered tight-binding models on two classes of rooted, high-dimensional graphs -- trees and hypercubes -- with a form of strong disorder correlations we term `radial disorder'. In this model, site energies on all sites equidistant from a chosen root are identical, while those at different distances are independent random variables (or their analogue for a deterministic but incommensurate potential, a case of which is also considered). Analytical arguments, supplemented by numerical results, are used to establish that this setting hosts robust and unusual multifractal states. The distribution of multifractality, as encoded in the inverse participation ratios (IPRs), is shown to be exceptionally broad. This leads to a qualitative difference in scaling with system size between the mean and typical IPRs, with the latter the appropriate quantity to characterise the multifractality. The existence of this multifractality is shown to be underpinned by an emergent fragmentation of the graphs into effective one-dimensional chains, which themselves exhibit conventional Anderson localisation. The interplay between the exponential localisation of states on these chains, and the exponential growth of the number of sites with distance from the root, is the origin of the observed multifractality.

cond-mat.dis-nn↗

arXiv2025

Partial projected ensembles and spatiotemporal structure of information scrambling

Thermalisation and information scrambling in out-of-equilibrium quantum many-body systems are deeply intertwined: local subsystems dynamically approach thermal density matrices while their entropies track information spreading. Projected ensembles--ensembles of pure states conditioned on measurement outcomes of complementary subsystems--provide higher-order probes of thermalisation, converging at late times to universal maximum-entropy ensembles. In this work, we introduce the partial projected ensemble (PPE) as a framework to study how the spatiotemporal structure of scrambling is imprinted on projected ensembles. The PPE consists of an ensemble of mixed states induced on a subsystem by measurements on a spatially separated part of its complement, tracing out the remainder, naturally capturing scenarios involving discarded outcomes or noise-induced losses. We show that statistical fluctuations of the PPE faithfully track the causal lightcone of information spreading, revealing how scrambling dynamics are encoded in ensemble structure. In addition, we demonstrate that the probabilities of bit-string probabilities (PoPs) associated with the PPE exhibit distinct dynamical regimes and provide an experimentally accessible probe of scrambling. Both PPE fluctuations and PoPs display exponential sensitivity to the size of the discarded region, reflecting exponential degradation of quantum correlations under erasure. We substantiate these findings using the non-integrable kicked Ising chain, combining numerics in the ergodic regime with exact results at its self-dual point. We extend our analysis to a many-body localised (MBL) regime numerically, along with analytic results for the $\ell$-bit model. The linear and logarithmic lightcones characteristic of ergodic and MBL regimes emerge naturally from PPE dynamics, establishing it as a powerful tool for probing scrambling and deep thermalisation.

quant-ph↗

arXiv2025

Do mixed states exhibit deep thermalisation?

Deep thermalisation -- where ensembles of pure states on a local subsystem, conditioned on measurement outcomes on its complement, approach universal maximum-entropy ensembles -- represents a stronger form of ergodicity than conventional thermalisation. We show that this framework fails dramatically for mixed initial states, evolved unitarily, even with infinitesimal initial mixedness. To address this, we introduce a new paradigm of deep thermalisation for mixed states, fundamentally distinct from that for pure-state ensembles. In our formulation, the deep thermal ensemble arises by tracing out auxiliary degrees of freedom from a maximum-entropy ensemble defined on an augmented system, with the ensemble structure depending explicitly on the entropy of the initial state. We demonstrate that such ensembles emerge dynamically in generic, locally interacting chaotic systems. For the self-dual kicked Ising chain, which we show to be exactly solvable for a class of mixed initial states, we find exact emergence of the so-defined mixed-state deep thermal ensemble at finite times. Our results therefore lead to fundamental insights into how maximum entropy principles and deep thermalisation manifest themselves in unitary dynamics of states with finite entropy.

quant-ph↗

arXiv2025

Imprints of information scrambling on eigenstates of a quantum chaotic system

How are the spatial and temporal patterns of information scrambling in locally interacting quantum many-body systems imprinted on the eigenstates of the system's time-evolution operator? We address this question by identifying statistical correlations among sets of minimally four eigenstates that provide a unified framework for various measures of information scrambling. These include operator mutual information and operator entanglement entropy of the time-evolution operator, as well as more conventional diagnostics such as two-point dynamical correlations and out-of-time-ordered correlators. We demonstrate this framework by deriving exact results for eigenstate correlations in a minimal model of quantum chaos -- Floquet dual-unitary circuits. These results reveal not only the butterfly effect and the information lightcone, but also finer structures of scrambling within the lightcone. Our work thus shows how the eigenstates of a chaotic system can encode the full spatiotemporal anatomy of quantum chaos, going beyond the descriptions offered by random matrix theory and the eigenstate thermalisation hypothesis.

quant-ph↗

arXiv2025

Logarithmic entanglement lightcone from eigenstate correlations in the many-body localised phase

We investigate the operator entanglement of the time-evolution operator through the framework of eigenstate correlations. Focusing on strongly disordered quantum many-body systems in the many-body localised (MBL) regime, we analyse the operator entanglement across various spatiotemporal cuts, revealing the logarithmic lightcone of entanglement spreading. We demonstrate that this logarithmic lightcone arises directly from a hierarchy of energyscales and lengthscales encoded in eigenstate correlations. By characterising the statistics of these hierarchical scales, we develop a microscopic theory for the spatiotemporal structure of entanglement spreading in MBL systems -- without invoking phenomenological constructs such as $\ell$-bits. This approach reveals the fundamental connection between eigenstate correlations and the emergent entanglement structure in MBL systems.

cond-mat.dis-nn↗

arXiv2025

Projected ensemble in a system with conserved charges with local support

The investigation of ergodicity or lack thereof in isolated quantum many-body systems has conventionally focused on the description of the reduced density matrices of local subsystems in the contexts of thermalization, integrability, and localization. Recent experimental capabilities to measure the full distribution of quantum states in Hilbert space and the emergence of specific state ensembles have extended this to questions of {\textit{deep thermalization}}, by introducing the notion of the {\textit{projected ensemble}} -- ensembles of pure states of a subsystem obtained by projective measurements on its complement. While previous work examined chaotic unitary circuits, Hamiltonian evolution, and systems with global conserved charges, we study the projected ensemble in systems where there are an extensive number of conserved charges all of which have (quasi)local support. We employ a strongly disordered quantum spin chain which shows many-body localized dynamics over long timescales as well as the $\ell$-bit model, a phenomenological archetype of a many-body localized system, with the charges being $1$-local in the latter. In particular, we discuss the dependence of the projected ensemble on the measurement basis. Starting with random direct product states, we find that the projected ensemble constructed from time-evolved states converges to a Scrooge ensemble at late times and in the large system limit except when the measurement operator is close to the conserved charges. This is in contrast to systems with global conserved charges where the ensemble varies continuously with the measurement basis. We relate these observations to the emergence of Porter-Thomas distribution in the probability distribution of bitstring measurement probabilities.

cond-mat.stat-mech↗

arXiv2024

Measurement-invisible quantum correlations in scrambling dynamics

Scrambling unitary dynamics in a quantum system transmutes local quantum information into a non-local web of correlations which manifests itself in a complex spatio-temporal pattern of entanglement. In such a context, we show there can exist three distinct dynamical phases characterised by qualitatively different forms of quantum correlations between two disjoint subsystems of the system. Transitions between these phases are driven by the relative sizes of the subsystems and the degree scrambling that the dynamics effects. Besides a phase which has no quantum correlations as manifested by vanishing entanglement between the parts and a phase which has non-trivial quantum correlations quantified by a finite entanglement monotone, we reveal a new phase transition within the entangled phase which separates phases wherein the quantum correlations are invisible or visible to measurements on one of the subsystems. This is encoded in the qualitatively different properties of the ensemble of states on one of the subsystems conditioned on the various measurement outcomes on the other subsystem. This provides a new characterisation of entanglement phases in terms of their response to measurements instead of the more ubiquitous measurement-induced entanglement transitions. Our results have implications for the kind of tasks that can be performed using measurement feedback within the framework of quantum interactive dynamics.

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