arXiv subjects

Arijeet Pal

Publications and source records attributed to Arijeet Pal.

At least 37 records · Page 2Linked to original sources

arXiv2023

Absence of localization in two-dimensional Clifford circuits

We analyze a Floquet circuit with random Clifford gates in one and two spatial dimensions. By using random graphs and methods from percolation theory, we prove in the two dimensional setting that some local operators grow at ballistic rate, which implies the absence of localization. In contrast, the one-dimensional model displays a strong form of localization characterized by the emergence of left and right-blocking walls in random locations. We provide additional insights by complementing our analytical results with numerical simulations of operator spreading and entanglement growth, which show the absence (presence) of localization in two-dimension (one-dimension). Furthermore, we unveil that the spectral form factor of the Floquet unitary in two-dimensional circuits behaves like that of quasi-free fermions with chaotic single particle dynamics, with an exponential ramp that persists till times scaling linearly with the size of the system. Our work sheds light on the nature of disordered, Floquet Clifford dynamics and its relationship to fully chaotic quantum dynamics.

quant-ph↗

arXiv2023

Transport and entanglement growth in long-range random Clifford circuits

Conservation laws can constrain entanglement dynamics in isolated quantum systems, manifest in a slowdown of higher Rényi entropies. Here, we explore this phenomenon in a class of long-range random Clifford circuits with U$(1)$ symmetry where transport can be tuned from diffusive to superdiffusive. We unveil that the different hydrodynamic regimes reflect themselves in the asymptotic entanglement growth according to $S(t) \propto t^{1/z}$, where the dynamical transport exponent $z$ depends on the probability $\propto r^{-α}$ of gates spanning a distance $r$. For sufficiently small $α$, we show that the presence of hydrodynamic modes becomes irrelevant such that $S(t)$ behaves similarly in circuits with and without conservation law. We explain our findings in terms of the inhibited operator spreading in U$(1)$-symmetric Clifford circuits, where the emerging light cones can be understood in the context of classical Lévy flights. Our work sheds light on the connections between Clifford circuits and more generic many-body quantum dynamics.

cond-mat.stat-mech↗

arXiv2022

Many-body localization and delocalization dynamics in the thermodynamic limit

Disordered quantum systems undergoing a many-body localization (MBL) transition fail to reach thermal equilibrium under their own dynamics. Distinguishing between asymptotically localized or delocalized dynamics based on numerical results is however nontrivial due to finite-size effects. Numerical linked cluster expansions (NLCE) provide a means to tackle quantum systems directly in the thermodynamic limit, but are challenging for models without translational invariance. Here, we demonstrate that NLCE provide a powerful tool to explore MBL by simulating quench dynamics in disordered spin-$1/2$ two-leg ladders and Fermi-Hubbard chains. Combining NLCE with an efficient real-time evolution of pure states, we obtain converged results for the decay of the imbalance on long time scales and show that, especially for intermediate disorder below the putative MBL transition, NLCE outperform direct simulations of finite systems with open or periodic boundaries. Furthermore, while spin is delocalized even in strongly disordered Hubbard chains with frozen charge, we unveil that an additional tilted potential leads to a drastic slowdown of the spin imbalance and nonergodic behavior on accessible times. Our work sheds light on MBL in systems beyond the well-studied disordered Heisenberg chain and emphasizes the usefulness of NLCE for this purpose.

cond-mat.stat-mech↗

arXiv2022

Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians

Atypical eigenstates in the form of quantum scars and fragmentation of Hilbert space due to conservation laws provide obstructions to thermalization in the absence of disorder. In certain models with dipole and $U(1)$ conservation, the fragmentation results in subdiffusive transport. In this paper we study the interplay between scarring and weak fragmentation giving rise to anomalous hydrodynamics in a class of one-dimensional spin-$1$ frustration-free projector Hamiltonians, known as deformed Motzkin chain. The ground states and low-lying excitations of these chains exhibit large entanglement and critical slowdown. We show that at high energies the particular form of the projectors causes the emergence of disjoint Krylov subspaces for open boundary conditions, with an exact quantum scar being embedded in each subspace, leading to slow growth of entanglement and localized dynamics for specific out-of-equilibrium initial states. Furthermore, focusing on infinite temperature, we unveil that spin transport is subdiffusive, which we corroborate by simulations of constrained stochastic cellular automaton circuits. Compared to dipole moment conserving systems, the deformed Motzkin chain appears to belong to a different universality class with distinct dynamical transport exponent and only polynomially many Krylov subspaces.

cond-mat.stat-mech↗

arXiv2021

Quantum simulation using noisy unitary circuits and measurements

Many-body quantum systems are notoriously hard to study theoretically due to the exponential growth of their Hilbert space. It is also challenging to probe the quantum correlations in many-body states in experiments due to their sensitivity to external noise. Using synthetic quantum matter to simulate quantum systems has opened new ways of probing quantum many-body systems with unprecedented control, and of engineering phases of matter which are otherwise hard to find in nature. Noisy quantum circuits have become an important cornerstone of our understanding of quantum many-body dynamics. In particular, random circuits act as minimally structured toy models for chaotic nonintegrable quantum systems, faithfully reproducing some of their universal properties. Crucially, in contrast to the full microscopic model, random circuits can be analytically tractable under a reasonable set of assumptions, thereby providing invaluable insights into questions which might be out of reach even for state-of-the-art numerical techniques. Here, we give an overview of two classes of dynamics studied using random-circuit models, with a particular focus on the dynamics of quantum entanglement. We will especially pay attention to potential near-term applications of random-circuit models on noisy-intermediate scale quantum (NISQ) devices. In this context, we cover hybrid circuits consisting of unitary gates interspersed with nonunitary projective measurements, hosting an entanglement phase transition from a volume-law to an area-law phase of the steady-state entanglement. Moreover, we consider random-circuit sampling experiments and discuss the usefulness of random quantum states for simulating quantum many-body dynamics on NISQ devices by leveraging the concept of quantum typicality. We highlight how emergent hydrodynamics can be studied by utilizing random quantum states generated by chaotic circuits.

quant-ph↗

arXiv2021

Measurement-induced criticality and entanglement clusters: a study of 1D and 2D Clifford circuits

Entanglement transitions in quantum dynamics present a novel class of phase transitions in non-equilibrium systems. When a many-body quantum system undergoes unitary evolution interspersed with monitored random measurements, the steady-state can exhibit a phase transition between volume and area-law entanglement. There is a correspondence between measurement-induced transitions in non-unitary quantum circuits in $d$ spatial dimensions and classical statistical mechanical models in $d+1$ dimensions. In certain limits these models map to percolation, but there is analytical and numerical evidence to suggest that away from these limits the universality class should generically be distinct from percolation. Intriguingly, despite these arguments, numerics on 1D qubit circuits give bulk exponents which are nonetheless close to those of 2D percolation, with possible differences in surface behavior. In the first part of this work we study the critical properties of 2D Clifford circuits. In the bulk, we find many properties suggested by the percolation picture, including matching bulk exponents, and an inverse power-law for the critical entanglement growth, $S(t,L) \sim L(1 - a/t)$, which saturates to an area-law. We then utilize a graph-state based algorithm to analyze in 1D and 2D the critical properties of entanglement clusters in the steady state. We show that in a model with a simple geometric map to percolation, the projective transverse field Ising model, the entanglement clusters are governed by percolation surface exponents. However, in the Clifford models we find large deviations in the cluster exponents from those of surface percolation, highlighting the breakdown of any possible geometric map to percolation. Given the evidence for deviations from the percolation universality class, our results raise the question of why nonetheless many bulk properties behave similarly to percolation.

quant-ph↗

arXiv2021

Quantum scars and bulk coherence in a symmetry-protected topological phase

Formation of quantum scars in many-body systems provides a novel mechanism for enhancing coherence of weakly entangled states. At the same time, coherence of edge modes in certain symmetry protected topological (SPT) phases can persist away from the ground state. In this work we show the existence of many-body scars and their implications on bulk coherence in such an SPT phase. To this end, we study the eigenstate properties and the dynamics of an interacting spin-$1/2$ chain with three-site "cluster" terms hosting a $\mathbb{Z}_2 \times \mathbb{Z}_2$ SPT phase. Focusing on the weakly interacting regime, we find that eigenstates with volume-law entanglement coexist with area-law entangled eigenstates throughout the spectrum. We show that a subset of the latter can be constructed by virtue of repeated cluster excitations on the even or odd sublattice of the chain, resulting in an equidistant "tower" of states, analogous to the phenomenology of quantum many-body scars. We further demonstrate that these scarred eigenstates support nonthermal expectation values of local cluster operators in the bulk and exhibit signatures of topological order even at finite energy densities. Studying the dynamics for out-of-equilibrium states drawn from the noninteracting "cluster basis", we unveil that nonthermalizing bulk dynamics can be observed on long time scales if clusters on odd and even sites are energetically detuned. In this case, cluster excitations remain essentially confined to one of the two sublattices such that inhomogeneous cluster configurations cannot equilibrate and thermalization of the full system is impeded. Our work sheds light on the role of quantum many-body scars in preserving SPT order at finite temperature and the possibility of coherent bulk dynamics in models with SPT order beyond the existence of long-lived edge modes.

cond-mat.stat-mech↗

arXiv2021

Frustration-induced emergent Hilbert space fragmentation

Although most quantum systems thermalize locally on short time scales independent of initial conditions, recent developments have shown this is not always the case. Lattice geometry and quantum mechanics can conspire to produce constrained quantum dynamics and associated glassy behavior, a phenomenon that falls outside the rubric of the eigenstate thermalization hypothesis. Constraints "fragment" the many-body Hilbert space due to which some states remain insulated from others and the system fails to attain thermal equilibrium. Such fragmentation is a hallmark of geometrically frustrated magnets with low-energy "icelike manifolds" exhibiting a broad range of relaxation times for different initial states. Focusing on the highly frustrated kagome lattice, we demonstrate these phenomena in the Balents-Fisher-Girvin Hamiltonian (easy-axis regime), and a three-coloring model (easy-plane regime), both with constrained Hilbert spaces. We study their level statistics and relaxation dynamics to develop a coherent picture of fragmentation in various limits of the XXZ model on the kagome lattice.

cond-mat.str-el↗

arXiv2021

Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits

In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the buildup of spatiotemporal correlation functions in one- and two-dimensional quantum spin systems, where we particularly scrutinize the inevitable impact of errors present in any realistic implementation. Importantly, we find that the hydrodynamic scaling of the correlations is highly robust with respect to the size of the Trotter step, which opens the door to reach nontrivial time scales with a small number of gates. While errors within the random circuit are shown to be irrelevant, we furthermore unveil that meaningful results can be obtained for noisy time evolutions with error rates achievable on near-term hardware. Our work emphasizes the practical relevance of random circuits on NISQ devices beyond the abstract sampling task.

cond-mat.stat-mech↗

arXiv2020

Measurement-induced entanglement transitions in many-body localized systems

The resilience of quantum entanglement to a classicality-inducing environment is tied to fundamental aspects of quantum many-body systems. The dynamics of entanglement has recently been studied in the context of measurement-induced entanglement transitions, where the steady-state entanglement collapses from a volume-law to an area-law at a critical measurement probability $p_{c}$. Interestingly, there is a distinction in the value of $p_{c}$ depending on how well the underlying unitary dynamics scramble quantum information. For strongly chaotic systems, $p_{c} > 0$, whereas for weakly chaotic systems, such as integrable models, $p_{c} = 0$. In this work, we investigate these measurement-induced entanglement transitions in a system where the underlying unitary dynamics are many-body localized (MBL). We demonstrate that the emergent integrability in an MBL system implies a qualitative difference in the nature of the measurement-induced transition depending on the measurement basis, with $p_{c} > 0$ when the measurement basis is scrambled and $p_{c} = 0$ when it is not. This feature is not found in Haar-random circuit models, where all local operators are scrambled in time. When the transition occurs at $p_{c} > 0$, we use finite-size scaling to obtain the critical exponent $ν= 1.3(2)$, close to the value for 2+0D percolation. We also find a dynamical critical exponent of $z = 0.98(4)$ and logarithmic scaling of the Rényi entropies at criticality, suggesting an underlying conformal symmetry at the critical point. This work further demonstrates how the nature of the measurement-induced entanglement transition depends on the scrambling nature of the underlying unitary dynamics. This leads to further questions on the control and simulation of entangled quantum states by measurements in open quantum systems.

quant-ph↗

arXiv2020

Exact three-colored quantum scars from geometric frustration

Non-equilibrium properties of quantum materials present many intriguing properties, among them athermal behavior, which violates the eigenstate thermalization hypothesis. Such behavior has primarily been observed in disordered systems. More recently, experimental and theoretical evidence for athermal eigenstates, known as "quantum scars" has emerged in non-integrable disorder-free models in one dimension with constrained dynamics. In this work, we show the existence of quantum scar eigenstates and investigate their dynamical properties in many simple two-body Hamiltonians with "staggered" interactions, involving ferromagnetic and antiferromagnetic motifs, in arbitrary dimensions. These magnetic models include simple modifications of widely studied ones (e.g., the XXZ model) on a variety of frustrated and unfrustrated lattices. We demonstrate our ideas by focusing on the two dimensional frustrated spin-1/2 kagome antiferromagnet, which was previously shown to harbor a special exactly solvable point with "three-coloring" ground states in its phase diagram. For appropriately chosen initial product states -- for example, those which correspond to any state of valid three-colors -- we show the presence of robust quantum revivals, which survive the addition of anisotropic terms. We also suggest avenues for future experiments which may see this effect in real materials.

cond-mat.str-el↗

arXiv2020

Signatures of the Many-body Localized Regime in Two Dimensions

Lessons from Anderson localization highlight the importance of dimensionality of real space for localization due to disorder. More recently, studies of many-body localization have focussed on the phenomenon in one dimension using techniques of exact diagonalization and tensor networks. On the other hand, experiments in two dimensions have provided concrete results going beyond the previously numerically accessible limits while posing several challenging questions. We present the first large-scale numerical examination of a disordered Bose-Hubbard model in two dimensions realized in cold atoms, which shows entanglement based signatures of many-body localization. By generalizing a low-depth quantum circuit to two dimensions we approximate eigenstates in the experimental parameter regimes for large systems, which is beyond the scope of exact diagonalization. A careful analysis of the eigenstate entanglement structure provides an indication of the putative phase transition marked by a peak in the fluctuations of entanglement entropy in a parameter range consistent with experiments.

cond-mat.dis-nn↗

arXiv2020

Behavior of l-bits near the many-body localization transition

Eigenstates of fully many-body localized (FMBL) systems are described by quasilocal operators $τ_i^z$ (l-bits), which are conserved exactly under Hamiltonian time evolution. The algebra of the operators $τ_i^z$ and $τ_i^x$ associated with l-bits ($\boldsymbolτ_i$) completely defines the eigenstates and the matrix elements of local operators between eigenstates at all energies. We develop a non-perturbative construction of the full set of l-bit algebras in the many-body localized phase for the canonical model of MBL. Our algorithm to construct the Pauli-algebra of l-bits combines exact diagonalization and a tensor network algorithm developed for efficient diagonalization of large FMBL Hamiltonians. The distribution of localization lengths of the l-bits is evaluated in the MBL phase and used to characterize the MBL-to-thermal transition.

cond-mat.dis-nn↗

arXiv2020

Approximating observables on eigenstates of large many-body localized systems

Eigenstates of fully many-body localized (FMBL) systems can be organized into spin algebras based on quasilocal operators called l-bits. These spin algebras define quasilocal l-bit measurement ($τ^z_i$) and l-bit flip ($τ^x_i$) operators. For a disordered Heisenberg spin chain in the MBL regime we approximate l-bit flip operators by finding them exactly on small windows of systems and extending them onto the whole system by exploiting their quasilocal nature. We subsequently use these operators to represent approximate eigenstates. We then describe a method to calculate products of local observables on these eigenstates for systems of size $L$ in $O(L^2)$ time. This algorithm is used to compute the error of the approximate eigenstates.

cond-mat.dis-nn↗

arXiv2019

Scale Invariant Entanglement Negativity at the Many-Body Localization Transition

The exact nature of the many-body localization transition remains an open question. An aspect which has been posited in various studies is the emergence of scale invariance around this point, however the direct observation of this phenomenon is still absent. Here we achieve this by studying the logarithmic negativity and mutual information between disjoint blocks of varying size across the many-body localization transition. The two length scales, block sizes and the distance between them, provide a clear quantitative probe of scale invariance across different length scales. We find that at the transition point, the logarithmic negativity obeys a scale invariant exponential decay with respect to the ratio of block separation to size, whereas the mutual information obeys a polynomial decay. The observed scale invariance of the quantum correlations in a microscopic model opens the direction to probe the fractal structure in critical eigenstates using tensor network techniques and provide constraints on the theory of the many-body localization transition.

cond-mat.dis-nn↗

arXiv2019

Dissipative discrete time crystals

Periodically driven quantum systems host a range of non-equilibrium phenomena which are unrealizable at equilibrium. Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a discrete time crystal, a putative quantum phase of matter. We present the observation of discrete time crystalline order in a driven system of paramagnetic $P$ -donor impurities in isotopically enriched $^{28}Si$ cooled below $10$ K. The observations exhibit a stable subharmonic peak at half the drive frequency which remains pinned even in the presence of pulse error, a signature of DTC order. We propose a theoretical model based on the paradigmatic central spin model which is in good agreement with experimental observations, and investigate the role of dissipation in the stabilisation of the DTC. Both experiment and theory indicate that the order in this system is primarily a dissipative effect, and which persists in the presence of spin-spin interactions. We present a theoretical phase diagram as a function of interactions and dissipation for the central spin model which is consistent with the experiments. This opens up questions about the interplay of coherent interaction and dissipation for time-translation symmetry breaking in many-body Floquet systems.

cond-mat.mes-hall↗

arXiv2017

Efficient representation of fully many-body localized systems using tensor networks

We propose a tensor network encoding the set of all eigenstates of a fully many-body localized system in one dimension. Our construction, conceptually based on the ansatz introduced in Phys. Rev. B 94, 041116(R) (2016), is built from two layers of unitary matrices which act on blocks of $\ell$ contiguous sites. We argue this yields an exponential reduction in computational time and memory requirement as compared to all previous approaches for finding a representation of the complete eigenspectrum of large many-body localized systems with a given accuracy. Concretely, we optimize the unitaries by minimizing the magnitude of the commutator of the approximate integrals of motion and the Hamiltonian, which can be done in a local fashion. This further reduces the computational complexity of the tensor networks arising in the minimization process compared to previous work. We test the accuracy of our method by comparing the approximate energy spectrum to exact diagonalization results for the random field Heisenberg model on 16 sites. We find that the technique is highly accurate deep in the localized regime and maintains a surprising degree of accuracy in predicting certain local quantities even in the vicinity of the predicted dynamical phase transition. To demonstrate the power of our technique, we study a system of 72 sites and we are able to see clear signatures of the phase transition. Our work opens a new avenue to study properties of the many-body localization transition in large systems.

cond-mat.dis-nn↗

arXiv2016

Electron spin-flip correlations due to nuclear dynamics in driven GaAs double dots

We present experimental data and associated theory for correlations in a series of experiments involving repeated Landau-Zener sweeps through the crossing point of a singlet state and a spin aligned triplet state in a GaAs double quantum dot containing two conduction electrons, which are loaded in the singlet state before each sweep, and the final spin is recorded after each sweep. The experiments reported here measure correlations on time scales from 4 $μ$s to 2 ms. When the magnetic field is aligned in a direction such that spin-orbit coupling cannot cause spin flips, the correlation spectrum has prominent peaks centered at zero frequency and at the differences of the Larmor frequencies of the nuclei, on top of a frequency-independent background. When the spin-orbit field is relevant, there are additional peaks, centered at the frequencies of the individual species. A theoretical model which neglects the effects of high-frequency charge noise correctly predicts the positions of the observed peaks, and gives a reasonably accurate prediction of the size of the frequency-independent background, but gives peak areas that are larger than the observed areas by a factor of two or more. The observed peak widths are roughly consistent with predictions based on nuclear dephasing times of the order of 60 $μ$s. However, there is extra weight at the lowest observed frequencies, which suggests the existence of residual correlations on the scale of 2 ms. We speculate on the source of these discrepancies.

cond-mat.mes-hall↗