arXiv subjects

Zlatko Papić

Publications and source records attributed to Zlatko Papić.

At least 55 records · Page 3Linked to original sources

arXiv2023

Characterization of variational quantum algorithms using free fermions

We study variational quantum algorithms from the perspective of free fermions. By deriving the explicit structure of the associated Lie algebras, we show that the Quantum Approximate Optimization Algorithm (QAOA) on a one-dimensional lattice -- with and without decoupled angles -- is able to prepare all fermionic Gaussian states respecting the symmetries of the circuit. Leveraging these results, we numerically study the interplay between these symmetries and the locality of the target state, and find that an absence of symmetries makes nonlocal states easier to prepare. An efficient classical simulation of Gaussian states, with system sizes up to $80$ and deep circuits, is employed to study the behavior of the circuit when it is overparameterized. In this regime of optimization, we find that the number of iterations to converge to the solution scales linearly with system size. Moreover, we observe that the number of iterations to converge to the solution decreases exponentially with the depth of the circuit, until it saturates at a depth which is quadratic in system size. Finally, we conclude that the improvement in the optimization can be explained in terms of better local linear approximations provided by the gradients.

quant-ph↗

arXiv2023

Superdiffusive Energy Transport in Kinetically Constrained Models

Universal nonequilibrium properties of isolated quantum systems are typically probed by studying transport of conserved quantities, such as charge or spin, while transport of energy has received considerably less attention. Here, we study infinite-temperature energy transport in the kinetically-constrained PXP model describing Rydberg atom quantum simulators. Our state-of-the-art numerical simulations, including exact diagonalization and time-evolving block decimation methods, reveal the existence of two distinct transport regimes. At moderate times, the energy-energy correlation function displays periodic oscillations due to families of eigenstates forming different su(2) representations hidden within the spectrum. These families of eigenstates generalize the quantum many-body scarred states found in previous works and leave an imprint on the infinite-temperature energy transport. At later times, we observe a broad superdiffusive transport regime that we attribute to the proximity of a nearby integrable point. Intriguingly, strong deformations of the PXP model by the chemical potential do not restore diffusion, but instead lead to a stable superdiffusive exponent $z\approx3/2$. Our results suggest constrained models to be potential hosts of novel transport regimes and call for developing an analytic understanding of their energy transport.

cond-mat.stat-mech↗

arXiv2023

Bridging quantum criticality via many-body scarring

Quantum dynamics in certain kinetically-constrained systems can display a strong sensitivity to the initial condition, wherein some initial states give rise to persistent quantum revivals -- a type of weak ergodicity breaking known as `quantum many-body scarring' (QMBS). Recent work [Phys.Rev.B 105, 125123 (2022)] pointed out that QMBS gets destroyed by tuning the system to a quantum critical point, echoing the disappearance of long-range order in the system's ground state at equilibrium. Here we show that this picture can be much richer in systems that display QMBS dynamics from a continuous family of initial conditions: as the system is tuned across the critical point while at the same time deforming the initial state, the dynamical signatures of QMBS at intermediate times can undergo an apparently smooth evolution across the equilibrium phase transition point. We demonstrate this using the PXP model -- a paradigmatic model of QMBS that has recently been realized in Rydberg atom arrays as well as ultracold bosonic atoms in a tilted optical lattice. Using exact diagonalization and matrix product state methods, we map out the dynamical phase diagram of the PXP model with the quenched chemical potential. We demonstrate the existence of a continuous family of initial states that give rise to QMBS and formulate a ramping protocol that can be used to prepare such states in experiment. Our results show the ubiquity of scarring in the PXP model and highlight its intriguing interplay with quantum criticality.

quant-ph↗

arXiv2022

Local density of states and particle entanglement in topological quantum fluids

The understanding of particle entanglement is an important goal in the studies of correlated quantum matter. The widely-used method of scanning tunneling spectroscopy -- which measures the local density of states (LDOS) of a many-body system by injecting or removing an electron from it -- is expected to be sensitive to particle entanglement. In this paper, we systematically investigate the relation between the particle entanglement spectrum (PES) and the LDOS of fractional quantum Hall (FQH) states, the paradigmatic strongly-correlated phases of electrons with topological order. Using exact diagonalization, we show that the counting of levels in both the LDOS and PES in the Jain sequence of FQH states can be predicted from the composite fermion theory. We point out the differences between LDOS and PES characterization of the bulk quasihole excitations, and we discuss the conditions under which the LDOS counting can be mapped to that of PES. Our results affirm that tunneling spectroscopy is a sensitive tool for identifying the nature of FQH states.

cond-mat.str-el↗

arXiv2022

Driving quantum many-body scars in the PXP model

Periodic driving has been established as a powerful technique for engineering novel phases of matter and intrinsically out-of-equilibrium phenomena such as time crystals. Recent work by Bluvstein et al. [Science 371, 1355 (2021)] has demonstrated that periodic driving can also lead to a significant enhancement of quantum many-body scarring, whereby certain non-integrable systems can display persistent quantum revivals from special initial states. Nevertheless, the mechanisms behind driving-induced scar enhancement remain poorly understood. Here we report a detailed study of the effect of periodic driving on the PXP model describing Rydberg atoms in the presence of a strong Rydberg blockade - the canonical static model of quantum many-body scarring. We show that periodic modulation of the chemical potential gives rise to a rich phase diagram, with at least two distinct types of scarring regimes that we distinguish by examining their Floquet spectra. We formulate a toy model, based on a sequence of square pulses, that accurately captures the details of the scarred dynamics and allows for analytical treatment in the large-amplitude and high-frequency driving regimes. Finally, we point out that driving with a spatially inhomogeneous chemical potential allows to stabilize quantum revivals from arbitrary initial states in the PXP model, via a mechanism similar to prethermalization.

cond-mat.quant-gas↗

arXiv2022

Extensive multipartite entanglement from su(2) quantum many-body scars

Recent experimental observation of weak ergodicity breaking in Rydberg atom quantum simulators has sparked interest in quantum many-body scars - eigenstates which evade thermalisation at finite energy densities due to novel mechanisms that do not rely on integrability or protection by a global symmetry. A salient feature of some quantum many-body scars is their sub-volume bipartite entanglement entropy. In this work we demonstrate that such exact many-body scars also possess extensive multipartite entanglement structure if they stem from an su(2) spectrum generating algebra. We show this analytically, through scaling of the quantum Fisher information, which is found to be super-extensive for exact scarred eigenstates in contrast to generic thermal states. Furthermore, we numerically study signatures of multipartite entanglement in the PXP model of Rydberg atoms, showing that extensive quantum Fisher information density can be generated dynamically by performing a global quench experiment. Our results identify a rich multipartite correlation structure of scarred states with significant potential as a resource in quantum enhanced metrology.

quant-ph↗

arXiv2022

Hypergrid subgraphs and the origin of scarred quantum walks in the many-body Hilbert space

Following the recent observation of wave function revivals in large Rydberg atom quantum simulators, much effort has focused on understanding the emergence of many-body scars in non-integrable quantum systems. Here we explore the origin of scarred wavefunction revivals in a family of models obtained by deforming the graph adjacency matrix of the PXP model - the effective model of Rydberg atoms in the strong Rydberg blockade regime. We consider deformations that either enhance the Rydberg constraint, ultimately resulting in an effective tight-binding model of two hypercubes joined at a single vertex, or relax the constraint until reaching the free spin-1/2 model. In the former case, we argue that the model of two joined hypercubes captures the essential features of many-body scarring present in the PXP model. On the other hand, relaxing the constraint leads to a sequence of new scarred models, some with more robust scarring signatures than the PXP model, as can be understood from the graph-theoretic viewpoint. Our results shed light on the nature of scarring in the PXP model by identifying its simple parent model, while also highlighting its distinction from the free-spin precession.

quant-ph↗

arXiv2022

Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers

Intermediate-scale quantum technologies provide new opportunities for scientific discovery, yet they also pose the challenge of identifying suitable problems that can take advantage of such devices in spite of their present-day limitations. In solid-state materials, fractional quantum Hall (FQH) phases continue to attract attention as hosts of emergent geometrical excitations analogous to gravitons, resulting from the non-perturbative interactions between the electrons. However, the direct observation of such excitations remains a challenge. Here, we identify a quasi-one-dimensional model that captures the geometric properties and graviton dynamics of FQH states. We then simulate geometric quench and the subsequent graviton dynamics on the IBM quantum computer using an optimally-compiled Trotter circuit with bespoke error mitigation. Moreover, we develop an efficient, optimal-control-based variational quantum algorithm that can efficiently simulate graviton dynamics in larger systems. Our results open a new avenue for studying the emergence of gravitons in a new class of tractable models on the existing quantum hardware.

quant-ph↗

arXiv2022

Fractional quantum Hall effect in semiconductor systems

The fractional quantum Hall (FQH) effect refers to the strongly-correlated phenomena and the associated quantum phases of matter realized in a two-dimensional gas of electrons placed in a large perpendicular magnetic field. In such systems, topology and quantum mechanics conspire to give rise to exotic physics that manifests via robust quantization of the Hall resistance. In this chapter, we provide an overview of the experimental phenomenology of the FQH effect in GaAs-based semiconductor materials and present its theoretical interpretations in terms of trial wave functions, composite fermion quasiparticles, and enigmatic non-Abelian states. We also highlight some recent developments, including the parton theory and the Dirac composite fermion field theory of FQH states, the role of anisotropy and geometrical degrees of freedom, and quantum entanglement in FQH fluids.

cond-mat.mes-hall↗

arXiv2022

Tuning between continuous time crystals and many-body scars in long-range XYZ spin chains

Persistent oscillatory dynamics in non-equilibrium many-body systems is a tantalizing manifestation of ergodicity breakdown that continues to attract much attention. Recent works have focused on two classes of such systems: discrete time crystals and quantum many-body scars (QMBS). While both systems host oscillatory dynamics, its origin is expected to be fundamentally different: discrete time crystal is a phase of matter which spontaneously breaks the $\mathbb{Z}_2$ symmetry of the external periodic drive, while QMBS span a subspace of non-thermalizing eigenstates forming an su(2) algebra representation. Here we ask a basic question: is there a physical system that allows to tune between these two dynamical phenomena? In contrast to much previous work, we investigate the possibility of a \emph{continuous} time crystal (CTC) in undriven, energy-conserving systems exhibiting prethermalization. We introduce a long-range XYZ spin model and show that it encompasses both a CTC phase as well as QMBS. We map out the dynamical phase diagram using numerical simulations based on exact diagonalization and time-dependent variational principle in the thermodynamic limit. We identify a regime where QMBS and CTC order co-exist, and we discuss experimental protocols that reveal their similarities as well as key differences.

cond-mat.str-el↗

arXiv2022

Prominent quantum many-body scars in a truncated Schwinger model

The high level of control and precision achievable in current synthetic quantum matter setups has enabled first attempts at quantum-simulating various intriguing phenomena in condensed matter physics, including those probing thermalization or its absence in closed quantum systems. In a recent work [Desaules \textit{et al.} [arXiv:2203.08830], we have shown that quantum many-body scars -- special low-entropy eigenstates that weakly break ergodicity in nonintegrable systems -- arise in spin-$S$ quantum link models that converge to $(1+1)-$D lattice quantum electrodynamics (Schwinger model) in the Kogut--Susskind limit $S\to\infty$. In this work, we further demonstrate that quantum many-body scars exist in a truncated version of the Schwinger model, and are qualitatively more prominent than their counterparts in spin-$S$ quantum link models. We illustrate this by, among other things, performing a finite-$S$ scaling analysis that strongly suggests that scarring persists in the truncated Schwinger model in the limit $S\to\infty$. Although it does not asymptotically converge to the Schwinger model, the truncated formulation is relevant to synthetic quantum matter experiments, and also provides fundamental insight into the nature of quantum many-body scars, their connection to lattice gauge theories, and the thermalization dynamics of the latter. Our conclusions can be readily tested in current cold-atom setups.

cond-mat.quant-gas↗

arXiv2022

Weak Ergodicity Breaking in the Schwinger Model

As a paradigm of weak ergodicity breaking in disorder-free nonintegrable models, quantum many-body scars (QMBS) can offer deep insights into the thermalization dynamics of gauge theories. Having been first discovered in a spin-$1/2$ quantum link formulation of the Schwinger model, it is a fundamental question as to whether QMBS persist for $S>1/2$ since such theories converge to the lattice Schwinger model in the large-$S$ limit, which is the appropriate version of lattice QED in one spatial dimension. In this work, we address this question by exploring QMBS in spin-$S$ $\mathrm{U}(1)$ quantum link models (QLMs) with staggered fermions. We find that QMBS persist at $S>1/2$, with the resonant scarring regime, which occurs for a zero-mass quench, arising from simple high-energy gauge-invariant initial states. We furthermore find evidence of detuned scarring regimes, which occur for finite-mass quenches starting in the physical vacua and the charge-proliferated state. Our results conclusively show that QMBS exist in a wide class of lattice gauge theories in one spatial dimension represented by spin-$S$ QLMs coupled to dynamical fermions.

cond-mat.str-el↗

arXiv2022

Very high-energy collective states of partons in fractional quantum Hall liquids

The low energy physics of fractional quantum Hall (FQH) states -- a paradigm of strongly correlated topological phases of matter -- to a large extent is captured by weakly interacting quasiparticles known as composite fermions (CFs). In this paper, based on numerical simulations and effective field theory, we argue that some \emph{high energy} states in the FQH spectra necessitate a different description based on \emph{parton} quasiparticles. We show that Jain states at filling factor $ν{=}n/(2pn\pm1)$ with integers $n,p{\geq}2$, support two kinds of collective modes: in addition to the well-known Girvin-MacDonald-Platzman (GMP) mode, they host a high energy collective mode, which is interpreted as the GMP mode of partons. We elucidate observable signatures of the parton mode in the dynamics following a geometric quench. We construct a microscopic wave function for the parton mode, and demonstrate agreement between its variational energy and exact diagonalization. Using the parton construction, we derive a field theory of the Jain states and show that the previously proposed effective theories follow from our approach. Our results point to partons being "real" quasiparticles which, in a way reminiscent of quarks, only become observable at sufficiently high energies.

cond-mat.str-el↗

arXiv2022

Many-body Hilbert space scarring on a superconducting processor

Quantum many-body scarring (QMBS) -- a recently discovered form of weak ergodicity breaking in strongly-interacting quantum systems -- presents opportunities for mitigating thermalization-induced decoherence in quantum information processsing. However, the existing experimental realizations of QMBS are based on kinetically-constrained systems where an emergent dynamical symmetry "shields" such states from the thermalizing bulk of the spectrum. Here, we experimentally realize a distinct kind of QMBS phenomena by approximately decoupling a part of the many-body Hilbert space in the computational basis. Utilizing a programmable superconducting processor with 30 qubits and tunable couplings, we realize Hilbert space scarring in a non-constrained model in different geometries, including a linear chain as well as a quasi-one-dimensional comb geometry. By performing full quantum state tomography on 4-qubit subsystems, we provide strong evidence for QMBS states by measuring qubit population dynamics, quantum fidelity and entanglement entropy following a quench from initial product states. Our experimental findings broaden the realm of QMBS mechanisms and pave the way to exploiting correlations in QMBS states for applications in quantum information technology.

quant-ph↗

arXiv2021

Bilayer WSe$_2$ as a natural platform for interlayer exciton condensates in the strong coupling limit

Exciton condensates (EC) are macroscopic coherent states arising from condensation of electron-hole pairs. Bilayer heterostructures, consisting of two-dimensional electron and hole layers separated by a tunnel barrier, provide a versatile platform to realize and study EC. The tunnel barrier suppresses recombination yielding long-lived excitons. However, this separation also reduces interlayer Coulomb interactions, limiting the exciton binding strength. Here, we report the observation of EC in naturally occurring 2H-stacked bilayer WSe$_2$. In this system, the intrinsic spin-valley structure suppresses interlayer tunneling even when the separation is reduced to the atomic limit, providing access to a previously unattainable regime of strong interlayer coupling. Using capacitance spectroscopy, we investigate magneto-EC, formed when partially filled Landau levels (LL) couple between the layers. We find that the strong-coupling EC show dramatically different behaviour compared with previous reports, including an unanticipated variation of the EC robustness with the orbital number, and find evidence for a transition between two types of low-energy charged excitations. Our results provide a demonstration of tuning EC properties by varying the constituent single-particle wavefunctions.

cond-mat.mes-hall↗

arXiv2021

A proposal for realising quantum scars in the tilted 1D Fermi-Hubbard model

Motivated by recent observations of ergodicity breaking due to Hilbert space fragmentation in 1D Fermi-Hubbard chains with a tilted potential [Scherg et al., arXiv:2010.12965], we show that the same system also hosts quantum many-body scars in a regime $U\approx Δ\gg J$ at electronic filling factor $ν=1$. We numerically demonstrate that the scarring phenomenology in this model is similar to other known realisations such as Rydberg atom chains, including persistent dynamical revivals and ergodicity-breaking many-body eigenstates. At the same time, we show that the mechanism of scarring in the Fermi-Hubbard model is different from other examples in the literature: the scars originate from a subgraph, representing a free spin-1 paramagnet, which is weakly connected to the rest of the Hamiltonian's adjacency graph. Our work demonstrates that correlated fermions in tilted optical lattices provide a platform for understanding the interplay of many-body scarring and other forms of ergodicity breaking, such as localisation and Hilbert space fragmentation.

cond-mat.str-el↗

arXiv2021

Weak ergodicity breaking through the lens of quantum entanglement

Recent studies of interacting systems of quantum spins, ultracold atoms and correlated fermions have shed a new light on how isolated many-body systems can avoid rapid equilibration to their thermal state. It has been shown that many such systems can "weakly" break ergodicity: they possess a small number of non-thermalising eigenstates and/or display slow relaxation from certain initial conditions, while majority of other initial states equilibrate fast, like in conventional thermalising systems. In this chapter, we provide a pedagogical introduction to weak ergodicity breaking phenomena, including Hilbert space fragmentation and quantum many-body scars. Central to these developments have been the tools based on quantum entanglement, in particular matrix product states and tangent space techniques, which have allowed to analytically construct non-thermal eigenstates in various non-integrable quantum models, and to explore semiclassical quantisation of such systems in the absence of a large-N or mean field limit. We also discuss recent experimental realisations of weak ergodicity breaking phenomena in systems of Rydberg atoms and tilted optical lattices.

cond-mat.quant-gas↗

arXiv2021

Emergence of Gaussianity in the thermodynamic limit of interacting fermions

Systems of interacting fermions can give rise to ground states whose correlations become effectively free-fermion-like in the thermodynamic limit, as shown by Baxter for a class of integrable models that include the one-dimensional XYZ spin-$\frac{1}{2}$ chain. Here, we quantitatively analyse this behaviour by establishing the relation between system size and correlation length required for the fermionic Gaussianity to emerge. Importantly, we demonstrate that this behaviour can be observed through the applicability of Wick's theorem and thus it is experimentally accessible. To establish the relevance of our results to possible experimental realisations of XYZ-related models, we demonstrate that the emergent Gaussianity is insensitive to weak variations in the range of interactions, coupling inhomogeneities and local random potentials.

cond-mat.str-el↗