arXiv subjects

Maksym Serbyn

Publications and source records attributed to Maksym Serbyn.

At least 55 records · Page 3Linked to original sources

arXiv2021

Quantum annealing initialization of the quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) is a prospective near-term quantum algorithm due to its modest circuit depth and promising benchmarks. However, an external parameter optimization required in QAOA could become a performance bottleneck. This motivates studies of the optimization landscape and search for heuristic ways of parameter initialization. In this work we visualize the optimization landscape of the QAOA applied to the MaxCut problem on random graphs, demonstrating that random initialization of the QAOA is prone to converging to local minima with sub-optimal performance. We introduce the initialization of QAOA parameters based on the Trotterized quantum annealing (TQA) protocol, parameterized by the Trotter time step. We find that the TQA initialization allows to circumvent the issue of false minima for a broad range of time steps, yielding the same performance as the best result out of an exponentially scaling number of random initializations. Moreover, we demonstrate that the optimal value of the time step coincides with the point of proliferation of Trotter errors in quantum annealing. Our results suggest practical ways of initializing QAOA protocols on near-term quantum devices and reveals new connections between QAOA and quantum annealing.

quant-ph↗

arXiv2021

Half and quarter metals in rhombohedral trilayer graphene

Ferromagnetism is most common in transition metal compounds but may also arise in low-density two-dimensional electron systems, with signatures observed in silicon, III-V semiconductor systems, and graphene moiré heterostructures. Here we show that gate-tuned van Hove singularities in rhombohedral trilayer graphene drive the spontaneous ferromagnetic polarization of the electron system into one or more spin- and valley flavors. Using capacitance measurements on graphite-gated van der Waals heterostructures, we find a cascade of density- and electronic displacement field tuned phase transitions marked by negative electronic compressibility. The transitions define the boundaries between phases where quantum oscillations have either four-fold, two-fold, or one-fold degeneracy, associated with a spin and valley degenerate normal metal, spin-polarized `half-metal', and spin and valley polarized `quarter metal', respectively. For electron doping, the salient features are well captured by a phenomenological Stoner model with a valley-anisotropic Hund's coupling, likely arising from interactions at the lattice scale. For hole filling, we observe a richer phase diagram featuring a delicate interplay of broken symmetries and transitions in the Fermi surface topology. Finally, by rotational alignment of a hexagonal boron nitride substrate to induce a moiré superlattice, we find that the superlattice perturbs the preexisting isospin order only weakly, leaving the basic phase diagram intact while catalyzing the formation of topologically nontrivial gapped states whenever itinerant half- or quarter metal states occur at half- or quarter superlattice band filling. Our results show that rhombohedral trilayer graphene is an ideal platform for well-controlled tests of many-body theory and reveal magnetism in moiré materials to be fundamentally itinerant in nature.

cond-mat.mes-hall↗

arXiv2021

Duality approach to quantum annealing of the 3-XORSAT problem

Classical models with complex energy landscapes represent a perspective avenue for the near-term application of quantum simulators. Until now, many theoretical works studied the performance of quantum algorithms for models with a unique ground state. However, when the classical problem is in a so-called clustering phase, the ground state manifold is highly degenerate. As an example, we consider a 3-XORSAT model defined on simple hypergraphs. The degeneracy of classical ground state manifold translates into the emergence of an extensive number of $Z_2$ symmetries, which remain intact even in the presence of a quantum transverse magnetic field. We establish a general duality approach that restricts the quantum problem to a given sector of conserved $Z_2$ charges and use it to study how the outcome of the quantum adiabatic algorithm depends on the hypergraph geometry. We show that the tree hypergraph which corresponds to a classically solvable instance of the 3-XORSAT problem features a constant gap, whereas the closed hypergraph encounters a second-order phase transition with a gap vanishing as a power-law in the problem size. The duality developed in this work provides a practical tool for studies of quantum models with classically degenerate energy manifold and reveals potential connections between glasses and gauge theories.

quant-ph↗

arXiv2021

Discrete time-crystalline order enabled by quantum many-body scars: entanglement steering via periodic driving

The control of many-body quantum dynamics in complex systems is a key challenge in the quest to reliably produce and manipulate large-scale quantum entangled states. Recently, quench experiments in Rydberg atom arrays (Bluvstein et. al., arXiv:2012.12276) demonstrated that coherent revivals associated with quantum many-body scars can be stabilized by periodic driving, generating stable subharmonic responses over a wide parameter regime. We analyze a simple, related model where these phenomena originate from spatiotemporal ordering in an effective Floquet unitary, corresponding to discrete time-crystalline (DTC) behavior in a prethermal regime. Unlike conventional DTC, the subharmonic response exists only for Neel-like initial states, associated with quantum scars. We predict robustness to perturbations and identify emergent timescales that could be observed in future experiments. Our results suggest a route to controlling entanglement in interacting quantum systems by combining periodic driving with many-body scars.

quant-ph↗

arXiv2021

Nonlinear orbital response across topological phase transition in centrosymmetric materials

Nonlinear optical responses are often used as a probe for studying electronic properties of materials. For topological materials, studies so far focused on the photogalvanic electric current, which requires breaking inversion symmetry. In this work we present a theory of orbital current response in inversion-symmetric topological insulators. We find a symmetry-allowed orbital current response that occurs in centrosymmetric materials under illumination by linearly polarized light. The sign of the dc nonlinear conductivity reflects the $\mathbb{Z}_2$ index and the conductivity changes sign at the transition between trivial and topological insulator phases. We derive an expression for the nonlinear orbital photocurrent for a general class of models with two doubly degenerate bands, and discuss its specific applications in the cases of the Bernevig-Hughes-Zhang model and the 1T' phase of transition metal dichalcogenides. Experimental setups for observation of the orbital current are also discussed.

cond-mat.mtrl-sci↗

arXiv2021

Entanglement view of dynamical quantum phase transitions

The analogy between an equilibrium partition function and the return probability in many-body unitary dynamics has led to the concept of dynamical quantum phase transition (DQPT). DQPTs are defined by non-analyticities in the return amplitude and are present in many models. In some cases DQPTs can be related to equilibrium concepts such as order parameters, yet their universal description is an open question. In this work we provide first steps towards a classification of DQPTs by using a matrix product state description of unitary dynamics in the thermodynamic limit. This allows us to distinguish the two limiting cases of precession and entanglement DQPTs, which are illustrated using an analytical description in the quantum Ising model. While precession DQPTs are characterized by a large entanglement gap and are semiclassical in their nature, entanglement DQPTs occur near avoided crossings in the entanglement spectrum and can be distinguished by a complex pattern of non-local correlations. We demonstrate the existence of precession and entanglement DQPTs beyond Ising model, discuss observables that can distinguish them and relate their interplay to complex DQPT phenomenology.

quant-ph↗

arXiv2020

Thouless Energy Across Many-Body Localization Transition in Floquet Systems

The notion of Thouless energy plays a central role in the theory of Anderson localization. We investigate the scaling of Thouless energy across the many-body localization (MBL) transition in a Floquet model. We use a combination of methods that are reliable on the ergodic side of the transition (e.g., spectral form factor) and methods that work on the MBL side (e.g. typical matrix elements of local operators) to obtain a complete picture of the Thouless energy behavior across the transition. On the ergodic side, the Thouless energy tends to a value independent of system size, while at the transition it becomes comparable to the level spacing. Different probes yield consistent estimates of the Thouless energy in their overlapping regime of applicability, giving the location of the transition point nearly free of finite-size drift. This work establishes a connection between different definitions of Thouless energy in a many-body setting, and yields new insights into the MBL transition in Floquet systems.

cond-mat.dis-nn↗

arXiv2020

Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays

Controlling non-equilibrium quantum dynamics in many-body systems is an outstanding challenge as interactions typically lead to thermalization and a chaotic spreading throughout Hilbert space. We experimentally investigate non-equilibrium dynamics following rapid quenches in a many-body system composed of 3 to 200 strongly interacting qubits in one and two spatial dimensions. Using a programmable quantum simulator based on Rydberg atom arrays, we probe coherent revivals corresponding to quantum many-body scars. Remarkably, we discover that scar revivals can be stabilized by periodic driving, which generates a robust subharmonic response akin to discrete time-crystalline order. We map Hilbert space dynamics, geometry dependence, phase diagrams, and system-size dependence of this emergent phenomenon, demonstrating novel ways to steer entanglement dynamics in many-body systems and enabling potential applications in quantum information science.

quant-ph↗

arXiv2020

Quantum Many-Body Scars and Weak Breaking of Ergodicity

Recent discovery of persistent revivals in quantum simulators based on Rydberg atoms have pointed to the existence of a new type of dynamical behavior that challenged the conventional paradigms of integrability and thermalization. This novel collective effect has been named quantum many-body scars by analogy with weak ergodicity breaking of a single particle inside a stadium billiard. In this overview, we provide a pedagogical introduction to quantum many-body scars and highlight the newly emerged connections with the semiclassical quantization of many-body systems. We discuss the relation between scars and more general routes towards weak violations of ergodicity due to "embedded" algebras and non-thermal eigenstates, and highlight possible applications of scars in quantum technology.

quant-ph↗

arXiv2020

Stability of mobility edges in disordered interacting systems

Many-body localization provides a mechanism to avoid thermalization in isolated interacting quantum systems. The breakdown of thermalization may be complete, when all eigenstates in the many-body spectrum become localized, or partial, when the so-called many-body mobility edge separates localized and delocalized parts of the spectrum. Previously, De Roeck \textit{et al.}[arXiv:1506.01505] suggested a possible instability of the many-body mobility edge in energy density. The local ergodic regions -- so called "bubbles" -- resonantly spread throughout the system, leading to delocalization. In order to study such instability mechanism, in this work we design a model featuring many-body mobility edge in \emph{particle density}: the states at small particle density are localized, while increasing the density of particles leads to delocalization. Using numerical simulations with matrix product states we demonstrate the stability of MBL with respect to small bubbles in large dilute systems for experimentally relevant timescales. In addition, we demonstrate that processes where the bubble spreads are favored over processes that lead to resonant tunneling, suggesting a possible mechanism behind the observed stability of many-body mobility edge. We conclude by proposing experiments to probe particle density mobility edge in Bose-Hubbard model.

cond-mat.dis-nn↗

arXiv2020

Gully quantum Hall ferromagnetism in biased trilayer graphene

Multilayer graphene lattices allow for an additional tunability of the band structure by the strong perpendicular electric field. In particular, the emergence of the new multiple Dirac points in ABA stacked trilayer graphene subject to strong transverse electric fields was proposed theoretically and confirmed experimentally. These new Dirac points dubbed ``gullies'' emerge from the interplay between strong electric field and trigonal warping. In this work we first characterize the properties of new emergent Dirac points and show that the electric field can be used to tune the distance between gullies in the momentum space. We demonstrate that the band structure has multiple Lifshitz transitions and higher-order singularity of ``monkey saddle'' type. Following the characterization of the band structure, we consider the spectrum of Landau levels and structure of their wave functions. In the limit of strong electric fields when gullies are well separated in momentum space, they give rise to triply degenerate Landau levels. In the second part of this work, we investigate how degeneracy between three gully Landau levels is lifted in presence of interactions. Within the Hartree-Fock approximation we show that the symmetry breaking state interpolates between fully gully polarized state that breaks $C_3$ symmetry at high displacement field, and the gully symmetric state when the electric field is decreased. The discontinuous transition between these two states is driven by enhanced inter-gully tunneling and exchange. We conclude by outlining specific experimental predictions for the existence of such a symmetry-breaking state.

cond-mat.mes-hall↗

arXiv2019

Probing many-body localization phase transition with superconducting circuits

Chains of superconducting circuit devices provide a natural platform for studies of synthetic bosonic quantum matter. Motivated by the recent experimental progress in realizing disordered and interacting chains of superconducting transmon devices, we study the bosonic many-body localization phase transition using the methods of exact diagonalization as well as matrix product state dynamics. We estimate the location of transition separating the ergodic and the many-body localized phases as a function of the disorder strength and the many-body on-site interaction strength. The main difference between the bosonic model realized by superconducting circuits and similar fermionic model is that the effect of the on-site interaction is stronger due to the possibility of multiple excitations occupying the same site. The phase transition is found to be robust upon including longer-range hopping and interaction terms present in the experiments. Furthermore, we calculate experimentally relevant local observables and show that their temporal fluctuations can be used to distinguish between the dynamics of Anderson insulator, many-body localization, and delocalized phases. While we consider unitary dynamics, neglecting the effects of dissipation, decoherence and measurement back action, the timescales on which the dynamics is unitary are sufficient for observation of characteristic dynamics in the many-body localized phase. Moreover, the experimentally available disorder strength and interactions allow for tuning the many-body localization phase transition, thus making the arrays of superconducting circuit devices a promising platform for exploring localization physics and phase transition.

quant-ph↗

arXiv2019

Kosterlitz-Thouless scaling at many-body localization phase transitions

We propose a scaling theory for the many-body localization (MBL) phase transition in one dimension, building on the idea that it proceeds via a 'quantum avalanche'. We argue that the critical properties can be captured at a coarse-grained level by a Kosterlitz-Thouless (KT) renormalization group (RG) flow. On phenomenological grounds, we identify the scaling variables as the density of thermal regions and the lengthscale that controls the decay of typical matrix elements. Within this KT picture, the MBL phase is a line of fixed points that terminates at the delocalization transition. We discuss two possible scenarios distinguished by the distribution of rare, fractal thermal inclusions within the MBL phase. In the first scenario, these regions have a stretched exponential distribution in the MBL phase. In the second scenario, the near-critical MBL phase hosts rare thermal regions that are power-law distributed in size. This points to the existence of a second transition within the MBL phase, at which these power-laws change to the stretched exponential form expected at strong disorder. We numerically simulate two different phenomenological RGs previously proposed to describe the MBL transition. Both RGs display a universal power-law length distribution of thermal regions at the transition with a critical exponent $α_c=2$, and continuously varying exponents in the MBL phase consistent with the KT picture.

cond-mat.dis-nn↗

arXiv2019

Many-body localization, thermalization, and entanglement

Thermalizing quantum systems are conventionally described by statistical mechanics at equilibrium. However, not all systems fall into this category, with many body localization providing a generic mechanism for thermalization to fail in strongly disordered systems. Many-body localized (MBL) systems remain perfect insulators at non-zero temperature, which do not thermalize and therefore cannot be described using statistical mechanics. In this Colloquium we review recent theoretical and experimental advances in studies of MBL systems, focusing on the new perspective provided by entanglement and non-equilibrium experimental probes such as quantum quenches. Theoretically, MBL systems exhibit a new kind of robust integrability: an extensive set of quasi-local integrals of motion emerges, which provides an intuitive explanation of the breakdown of thermalization. A description based on quasi-local integrals of motion is used to predict dynamical properties of MBL systems, such as the spreading of quantum entanglement, the behavior of local observables, and the response to external dissipative processes. Furthermore, MBL systems can exhibit eigenstate transitions and quantum orders forbidden in thermodynamic equilibrium. We outline the current theoretical understanding of the quantum-to-classical transition between many-body localized and ergodic phases, and anomalous transport in the vicinity of that transition. Experimentally, synthetic quantum systems, which are well-isolated from an external thermal reservoir, provide natural platforms for realizing the MBL phase. We review recent experiments with ultracold atoms, trapped ions, superconducting qubits, and quantum materials, in which different signatures of many-body localization have been observed. We conclude by listing outstanding challenges and promising future research directions.

cond-mat.dis-nn↗

arXiv2019

Analytically solvable renormalization group for the many-body localization transition

We introduce a simple, exactly solvable strong-randomness renormalization group (RG) model for the many-body localization (MBL) transition in one dimension. Our approach relies on a family of RG flows parametrized by the asymmetry between thermal and localized phases. We identify the physical MBL transition in the limit of maximal asymmetry, reflecting the instability of MBL against rare thermal inclusions. We find a critical point that is localized with power-law distributed thermal inclusions. The typical size of critical inclusions remains finite at the transition, while the average size is logarithmically diverging. We propose a two-parameter scaling theory for the many-body localization transition that falls into the Kosterlitz-Thouless universality class, with the MBL phase corresponding to a stable line of fixed points with multifractal behavior.

cond-mat.dis-nn↗

arXiv2018

Emergent SU(2) dynamics and perfect quantum many-body scars

Motivated by recent experimental observations of coherent many-body revivals in a constrained Rydberg atom chain, we construct a weak quasi-local deformation of the Rydberg blockade Hamiltonian, which makes the revivals virtually perfect. Our analysis suggests the existence of an underlying non-integrable Hamiltonian which supports an emergent SU(2)-spin dynamics within a small subspace of the many-body Hilbert space. We show that such perfect dynamics necessitates the existence of atypical, nonergodic energy eigenstates - quantum many-body scars. Furthermore, using these insights, we construct a toy model that hosts exact quantum many-body scars, providing an intuitive explanation of their origin. Our results offer specific routes to enhancing coherent many-body revivals, and provide a step towards establishing the stability of quantum many-body scars in the thermodynamic limit.

quant-ph↗

arXiv2018

Emergent Dirac gullies and gully-symmetry breaking quantum Hall states in ABA trilayer graphene

We report on quantum capacitance measurements of high quality, graphite- and hexagonal boron nitride encapsulated Bernal stacked trilayer graphene devices. At zero applied magnetic field, we observe a number of electron density- and electrical displacement-tuned features in the electronic compressibility associated with changes in Fermi surface topology. At high displacement field and low density, strong trigonal warping gives rise to emergent Dirac gullies centered near the corners of the hexagonal Brillouin and related by three fold rotation symmetry. At low magnetic fields of $B=1.25$~T, the gullies manifest as a change in the degeneracy of the Landau levels from two to three. Weak incompressible states are also observed at integer filling within these triplets Landau levels, which a Hartree-Fock analysis indicates are associated with Coulomb-driven nematic phases that spontaneously break rotation symmetry.

cond-mat.mes-hall↗

arXiv2018

Detection and characterization of Many-Body Localization in Central Spin Models

We analyze a disordered central spin model, where a central spin interacts equally with each spin in a periodic one dimensional random-field Heisenberg chain. If the Heisenberg chain is initially in the many-body localized (MBL) phase, we find that the coupling to the central spin suffices to delocalize the chain for a substantial range of coupling strengths. We calculate the phase diagram of the model and identify the phase boundary between the MBL and ergodic phase. Within the localized phase, the central spin significantly enhances the rate of the logarithmic entanglement growth and its saturation value. We attribute the increase in entanglement entropy to a non-extensive enhancement of magnetization fluctuations induced by the central spin. Finally, we demonstrate that correlation functions of the central spin can be utilized to distinguish between MBL and ergodic phases of the 1D chain. Hence, we propose the use of a central spin as a possible experimental probe to identify the MBL phase.

cond-mat.dis-nn↗