arXiv subjects

Sthitadhi Roy

Publications and source records attributed to Sthitadhi Roy.

At least 37 records · Page 2Linked to original sources

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

Entanglement dynamics and eigenstate correlations in strongly disordered quantum many-body systems

The many-body localised phase of quantum systems is an unusual dynamical phase wherein the system fails to thermalise and yet, entanglement grows unboundedly albeit very slowly in time. We present a microscopic theory of this ultraslow growth of entanglement in terms of dynamical eigenstate correlations of strongly disordered, interacting quantum systems in the many-body localised regime. These correlations involve sets of four or more eigenstates and hence, go beyond correlations involving pairs of eigenstates which are usually studied in the context of eigenstate thermalisation or lack thereof. We consider the minimal case, namely the second Rényi entropy of entanglement, of an initial product state as well as that of the time-evolution operator, wherein the correlations involve quartets of four eigenstates. We identify that the dynamics of the entanglement entropy is dominated by the spectral correlations within certain special quartets of eigenstates. We uncover the spatial structure of these special quartets and the ensuing statistics of the spectral correlations amongst the eigenstates therein, which reveals a hierarchy of timescales or equivalently, energyscales. We show that the hierarchy of these timescales along with their non-trivial distributions conspire to produce the logarithmic in time growth of entanglement, characteristic of the many-body localised regime. The underlying spatial structures in the set of special quartets also provides a microscopic understanding of the spacetime picture of the entanglement growth. The theory therefore provides a much richer perspective on entanglement growth in strongly disordered systems compared to the commonly employed phenomenological approach based on the $\ell$-bit picture.

cond-mat.dis-nn↗

arXiv2024

The Fock-space landscape of many-body localisation

This article reviews recent progress in understanding the physics of many-body localisation (MBL) in disordered and interacting quantum many-body systems, from the perspective of ergodicity breaking on the associated Fock space. This approach to MBL is underpinned by mapping the dynamics of the many-body system onto that of a fictitious single particle on the high-dimensional, correlated and disordered Fock-space graph; yet, as we elaborate, the problem is fundamentally different from that of conventional Anderson localisation on high-dimensional or hierarchical graphs. We discuss in detail the nature of eigenstate correlations on the Fock space, both static and dynamic, and in the ergodic and many-body localised phases as well as in the vicinity of the MBL transition. The latter in turn sheds light on the nature of the transition, and motivates a scaling theory for it in terms of Fock-space based quantities. We also illustrate how these quantities can be concretely connected to real-space observables. An overview is given of several analytical and numerical techniques which have proven important in developing a comprehensive picture. Finally, we comment on some open questions in the field of MBL where the Fock-space approach is likely to prove insightful.

cond-mat.dis-nn↗

arXiv2023

The connection between Hilbert-space return probability and real-space autocorrelations in quantum spin chains

The dynamics of interacting quantum many-body systems has two seemingly disparate but fundamental facets. The first is the dynamics of real-space local observables, and if and how they thermalise. The second is to interpret the dynamics of the many-body state as that of a fictitious particle on the underlying Hilbert-space graph. In this work, we derive an explicit connection between these two aspects of the dynamics. We show that the temporal decay of the autocorrelation in a disordered quantum spin chain is explicitly encoded in how the return probability on Hilbert space approaches its late-time saturation. As such, the latter has the same functional form in time as the decay of autocorrelations but with renormalised parameters. Our analytical treatment is rooted in an understanding of the morphology of the time-evolving state on the Hilbert-space graph, and corroborated by exact numerical results.

cond-mat.dis-nn↗

arXiv2023

Eigenvector Correlations Across the Localisation Transition in non-Hermitian Power-Law Banded Random Matrices

The dynamics of non-Hermitian quantum systems have taken on an increasing relevance in light of quantum devices which are not perfectly isolated from their environment. The interest in them also stems from their fundamental differences from their Hermitian counterparts, particularly with regard to their spectral and eigenvector correlations. These correlations form the fundamental building block for understanding the dynamics of quantum systems as all other correlations can be reconstructed from it. In this work, we study such correlations across a localisation transition in non-Hermitian quantum systems. As a concrete setting, we consider non-Hermitian power-law banded random matrices which have emerged as a promising platform for studying localisation in disordered, non-Hermitian systems. We show that eigenvector correlations show marked differences between the delocalised and localised phases. In the delocalised phase, the eigenvectors are strongly correlated as evinced by divergent correlations in the limit of vanishingly small complex eigenvalue spacings. On the contrary, in the localised phase, the correlations are independent of the eigenvalue spacings. We explain our results in the delocalised phase by appealing to the Ginibre random matrix ensemble. On the other hand, in the localised phase, an analytical treatment sheds light on the suppressed correlations, relative to the delocalised phase. Given that eigenvector correlations are fundamental ingredients towards understanding real- and imaginary-time dynamics with non-Hermitian generators, our results open a new avenue for characterising dynamical phases in non-Hermitian quantum many-body systems.

cond-mat.dis-nn↗

arXiv2023

Anatomy of localisation protected quantum order on Hilbert space

Many-body localised phases of disordered, interacting quantum systems allow for exotic localisation protected quantum order in eigenstates at arbitrarily high energy densities. In this work, we analyse the manifestation of such order on the Hilbert-space anatomy of eigenstates. Quantified in terms of non-local Hilbert-spatial correlations of eigenstate amplitudes, we find that the spread of the eigenstates on the Hilbert-space graph is directly related to the order parameters which characterise the localisation protected order, and hence these correlations, in turn, characterise the order or lack thereof. Higher-point eigenstate correlations also characterise the different entanglement structures in the many-body localised phases, with and without order, as well as in the ergodic phase. The results pave the way for characterising the transitions between many-body localised phases and the ergodic phase in terms of scaling of emergent correlation lengthscales on the Hilbert-space graph.

cond-mat.dis-nn↗

arXiv2022

Probability transport on the Fock space of a disordered quantum spin chain

Within the broad theme of understanding the dynamics of disordered quantum many-body systems, one of the simplest questions one can ask is: given an initial state, how does it evolve in time on the associated Fock-space graph, in terms of the distribution of probabilities thereon? A detailed quantitative description of the temporal evolution of out-of-equilibrium disordered quantum states and probability transport on the Fock space, is our central aim here. We investigate it in the context of a disordered quantum spin chain which hosts a disorder-driven many-body localisation transition. Real-time dynamics/probability transport is shown to exhibit a rich phenomenology, which is markedly different between the ergodic and many-body localised phases. The dynamics is for example found to be strongly inhomogeneous at intermediate times in both phases, but while it gives way to homogeneity at long times in the ergodic phase, the dynamics remain inhomogeneous and multifractal in nature for arbitrarily long times in the localised phase. Similarly, we show that an appropriately defined dynamical lengthscale on the Fock-space graph is directly related to the local spin-autocorrelation, and as such sheds light on the (anomalous) decay of the autocorrelation in the ergodic phase, and lack of it in the localised phase.

cond-mat.dis-nn↗

arXiv2022

Hilbert-space correlations beyond multifractality and bipartite entanglement in many-body localised systems

Eigenstates of many-body localised (MBL) systems are characterised by area-law bipartite entanglement along with multifractal statistics of their amplitudes on Hilbert space. At the same time, sparse random pure states with fractal statistics are not compatible with area-law and necessarily exhibit volume-law entanglement. This raises the question that what correlation functions of Hilbert-space amplitudes MBL eigenstates must possess for their area law entanglement to be compatible with their multifractality. In this work, we identify and compute such appropriate Hilbert-space correlations which carry information of entanglement. We find that, for MBL eigenstates, these correlations are qualitatively different not only from those of ergodic states but also of sparse random states with fractal statistics. This enables us to show that indeed the said correlations lie at the heart of the coexistence of area-law entanglement and multifractality for MBL eigenstates.

cond-mat.dis-nn↗

arXiv2022

Arresting classical many-body chaos by kinetic constraints

We investigate the effect of kinetic constraints on classical many-body chaos in a translationally-invariant Heisenberg spin chain using a classical counterpart of the out-of-time-ordered correlator (OTOC). The strength of the constraint drives a 'dynamical phase transition' separating a delocalised phase, where the classical OTOC propagates ballistically, from a localised phase, where the OTOC does not propagate at all and the entire system freezes. This is unexpected given that all spins configurations are dynamically connected to each other. We show that localisation arises due to the dynamical formation of frozen islands, contiguous segments of spins immobile due to the constraints, dominating over the melting of such islands.

cond-mat.stat-mech↗

arXiv2022

Constrained Dynamics and Directed Percolation

In a recent work [A. Deger et al., Phys. Rev. Lett. 129, 160601 (2022)] we have shown that kinetic constraints can completely arrest many-body chaos in the dynamics of a classical, deterministic, translationally-invariant spin system with the strength of the constraint driving a dynamical phase transition. Using extensive numerical simulations and scaling analyses we demonstrate here that this constraint-induced phase transition lies in the directed percolation universality class in both one and two spatial dimensions.

cond-mat.stat-mech↗

arXiv2022

Absolutely Stable Spatiotemporal Order in Noisy Quantum Systems

We introduce a model of non-unitary quantum dynamics that exhibits infinitely long-lived discrete spatiotemporal order robust against any unitary or dissipative perturbation. Ergodicity is evaded by combining a sequence of projective measurements with a local feedback rule that is inspired by Toom's `North-East-Center' classical cellular automaton. The measurements in question only partially collapse the wavefunction of the system, allowing some quantum coherence to persist. We demonstrate our claims using numerical simulations of a Clifford circuit in two spatial dimensions which allows access to large system sizes, and also present results for more generic dynamics on modest system sizes. We also devise explicit experimental protocols realising this dynamics using one- and two-qubit gates that are available on present-day quantum computing platforms.

quant-ph↗

arXiv2022

Scaling of Fock-space propagator and multifractality across the many-body localization transition

We implement a recursive Green function method to extract the Fock space (FS) propagator and associated self-energy across the many-body localization (MBL) transition, for one-dimensional interacting fermions in a random onsite potential. We show that the typical value of the imaginary part of the local FS self-energy, Δ_t, related to the decay rate of an initially localized state, acts as a probabilistic order parameter for the thermal to MBL phase transition; and can be used to characterize critical properties of the transition as well as the multifractal nature of MBL states as a function of disorder strength W. In particular, we show that a fractal dimension D_s extracted from Δ_t jumps discontinuously across the transition, from D_s<1 in the MBL phase to D_s= 1 in the thermal phase. Moreover, Δ_t follows an asymmetrical finite-size scaling form across the thermal-MBL transition, where a non-ergodic volume in the thermal phase diverges with a Kosterlitz-Thouless like essential singularity at the critical point W_c, and controls the continuous vanishing of Δ_t as W_c is approached. In contrast, a correlation length (ξ) extracted from Δ_t exhibits a power-law divergence on approaching W_c from the MBL phase.

cond-mat.dis-nn↗

arXiv2022

Resonant energy scales and local observables in the many-body localised phase

We formulate a theory for resonances in the many-body localised (MBL) phase of disordered quantum spin chains in terms of local observables. A key result is to show that there are universal correlations between the matrix elements of local observables and the many-body level spectrum. This reveals how the matrix elements encode the energy scales associated with resonance, thereby allowing us to show that these energies are power-law distributed. Using these results we calculate analytically the distributions of local polarisations and of eigenstate fidelity susceptibilities. The first of these quantities characterises the proximity of MBL systems to noninteracting ones, while the second highlights their extreme sensitivity to local perturbations. Our theoretical approach is to consider the effect of varying a local field, which induces a parametric dynamics of spectral properties. We corroborate our results numerically using exact diagonalisation in finite systems.

cond-mat.dis-nn↗

arXiv2022

Real-time correlators in chaotic quantum many-body systems

We study real-time local correlators $\langle\mathcal{O}(\mathbf{x},t)\mathcal{O}(0,0)\rangle$ in chaotic quantum many-body systems. These correlators show universal structure at late times, determined by the dominant operator-space Feynman trajectories for the evolving operator $\mathcal{O}(\mathbf{x},t)$. The relevant trajectories involve the operator contracting to a point at both the initial and final time and so are structurally different from those dominating the out-of-time-order correlator. In the absence of conservation laws, correlations decay exponentially: $\langle\mathcal{O}(\mathbf{x},t)\mathcal{O}(0,0)\rangle\sim\exp(-s_\mathrm{eq} r(\mathbf{v}) t)$, where $\mathbf{v}= \mathbf{x}/ t$ defines a spacetime ray, and $r(\mathbf{v})$ is an associated decay rate. We express $r(\mathbf{v})$ in terms of cost functions for various spacetime structures. In 1+1D, operator histories can show a phase transition at a critical ray velocity $v_c$, where $r(\mathbf{v})$ is nonanalytic. At low $v$, the dominant Feynman histories are "fat": the operator grows to a size of order $t^α\gg 1$ before contracting to a point again. At high $v$ the trajectories are "thin": the operator always remains of order-one size. In a Haar-random unitary circuit, this transition maps to a simple binding transition for a pair of random walks (the two spatial boundaries of the operator). In higher dimensions, thin trajectories always dominate. We discuss ways to extract the butterfly velocity $v_B$ from the time-ordered correlator, rather than the OTOC. Correlators in the random circuit may alternatively be computed with an effective Ising-like model: a special feature of the Ising weights for the Haar brickwork circuit gives $v_c=v_B$. This work addresses lattice models, but also suggests the possibility of morphological phase transitions for real-time Feynman diagrams in quantum field theories.

cond-mat.stat-mech↗

arXiv2022

Anomalous multifractality in quantum chains with strongly correlated disorder

We demonstrate numerically that a robust and unusual multifractal regime can emerge in a one-dimensional quantum chain with maximally correlated disorder, above a threshold disorder strength. This regime is preceded by a mixed and an extended regime at weaker disorder strengths, with the former hosting both extended and multifractal eigenstates. The multifractal states we find are markedly different from conventional multifractal states in their structure, as they reside approximately uniformly over a continuous segment of the chain, and the lengths of these segments scale non-trivially with system size. This anomalous nature also leaves imprints on dynamics. An initially localised wavepacket shows ballistic transport, in contrast to the slow, generally sub-diffusive, transport commonly associated with multifractality. However, the timescale over which this ballistic transport persists again scales non-trivially with the system size.

cond-mat.dis-nn↗

arXiv2021

Local resonances and parametric level dynamics in the many-body localised phase

By varying the disorder realisation in the many-body localised (MBL) phase, we investigate the influence of resonances on spectral properties. The standard theory of the MBL phase is based on the existence of local integrals of motion (LIOM), and eigenstates of the time evolution operator can be described as LIOM configurations. We show that smooth variations of the disorder give rise to avoided level crossings, and we identify these with resonances between LIOM configurations. Through this parametric approach, we develop a theory for resonances in terms of standard properties of non-resonant LIOM. This framework describes resonances that are locally pairwise, and is appropriate in arbitrarily large systems deep within the MBL phase. We show that resonances are associated with large level curvatures on paths through the ensemble of disorder realisations, and we determine the curvature distribution. By considering the level repulsion associated with resonances we calculate the two-point correlator of the level density. We also find the distributions of matrix elements of local observables and discuss implications for low-frequency dynamics.

cond-mat.dis-nn↗

arXiv2021

Fock-space anatomy of eigenstates across the many-body localisation transition

We explore the Fock-space structure of eigenstates across the many-body localisation (MBL) transition in a disordered, interacting quantum spin-1/2 chain. Eigenstate expectation values of spatially local observables, which distinguish an MBL phase from an ergodic one, can be represented in terms of eigenstate amplitudes on the Fock space. Motivated by this, we introduce and study spatial correlations on the Fock space. From these, a correlation length emerges, which is found to vary discontinuously across the MBL transition; and is intimately connected to the discontinuous jump in the multifractal exponents characterising the Fock-space wavefunctions. Exploiting the direct connection between the local observables and Fock-space correlations, we show that the discontinuity in the lengthscale also implies discontinuous behaviour of the local observables across the transition. A scaling theory based on these Fock-space correlations is constructed, which is closely connected to that for the inverse participation ratio. It yields a volume-scale in the ergodic phase and a length-scale in the MBL phase, whose critical properties suggest a Kosterlitz-Thouless-like scenario for the MBL transition, as is predicted by recent phenomenological theories. Finally, we also show how correlation functions on the Fock space reveal the inhomogeneities in eigenstate amplitudes on the Fock space in the MBL phase.

cond-mat.dis-nn↗

arXiv2021

Localisation in quasiperiodic chains: a theory based on convergence of local propagators

Quasiperiodic systems serve as fertile ground for studying localisation, due to their propensity already in one dimension to exhibit rich phase diagrams with mobility edges. The deterministic and strongly-correlated nature of the quasiperiodic potential nevertheless offers challenges distinct from disordered systems. Motivated by this, we present a theory of localisation in quasiperiodic chains with nearest-neighbour hoppings, based on the convergence of local propagators; exploiting the fact that the imaginary part of the associated self-energy acts as a probabilistic order parameter for localisation transitions and, importantly, admits a continued-fraction representation. Analysing the convergence of these continued fractions, localisation or its absence can be determined, yielding in turn the critical points and mobility edges. Interestingly, we find anomalous scalings of the order parameter with system size at the critical points, consistent with the fractal character of critical eigenstates. Self-consistent theories at high orders are also considered, shown to be conceptually connected to the theory based on continued fractions, and found in practice to converge to the same result. Results are exemplified by analysing the theory for three quasiperiodic models covering a range of behaviour.

cond-mat.dis-nn↗