arXiv subjects

Maksym Serbyn

Publications and source records attributed to Maksym Serbyn.

At least 73 records · Page 4Linked to original sources

arXiv2017

Quantum many-body scars

Certain wave functions of non-interacting quantum chaotic systems can exhibit "scars" in the fabric of their real-space density profile. Quantum scarred wave functions concentrate in the vicinity of unstable periodic classical trajectories. We introduce the notion of many-body quantum scars which reflect the existence of a subset of special many-body eigenstates concentrated in certain parts of the Hilbert space. We demonstrate the existence of scars in the Fibonacci chain -- the one- dimensional model with a constrained local Hilbert space realized in the 51 Rydberg atom quantum simulator [H. Bernien et al., arXiv:1707.04344]. The quantum scarred eigenstates are embedded throughout the thermalizing many-body spectrum, but surprisingly lead to direct experimental signatures such as robust oscillations following a quench from a charge-density wave state found in experiment. We develop a model based on a single particle hopping on the Hilbert space graph, which quantitatively captures the scarred wave functions up to large systems of L = 32 atoms. Our results suggest that scarred many-body bands give rise to a new universality class of quantum dynamics, which opens up opportunities for creating and manipulating novel states with long-lived coherence in systems that are now amenable to experimental study.

quant-ph↗

arXiv2017

Non-interacting central site model: localization and logarithmic entanglement growth

We investigate the stationary and dynamical behavior of an Anderson localized chain coupled to a single central bound state. The coupling to the central site partially dilutes the Anderson localized peak towards the nearly resonant sites. In particular, the number of resonantly coupled sites remains finite in the thermodynamic limit. This is further supported by a multifractal analysis of eigenstates that shows the frozen spectrum of fractal dimension, which is characteristic for localized phases in models with power-law hopping. Although the well-known Fano-resonance problem is seemingly similar to our system, it fails to describe it because of the absence of level repulsion within the energy spectrum. For weak coupling strengths to the central site, we identify a regime with a logarithmic in time transport of particles and information.

cond-mat.dis-nn↗

arXiv2017

Loschmidt Echo in Many-Body Localized Phase

The Loschmidt echo, defined as the overlap between quantum wave function evolved with different Hamiltonians, quantifies the sensitivity of quantum dynamics to perturbations and is often used as a probe of quantum chaos. In this work we consider the behavior of the Loschmidt echo in the many body localized phase, which is characterized by emergent local integrals of motion, and provides a generic example of non-ergodic dynamics. We demonstrate that the fluctuations of the Loschmidt echo decay as a power law in time in the many-body localized phase, in contrast to the exponential decay in few-body ergodic systems. We consider the spin-echo generalization of the Loschmidt echo, and argue that the corresponding correlation function saturates to a finite value in localized systems. Slow, power-law decay of fluctuations of such spin-echo-type overlap is related to the operator spreading and is present only in the many-body localized phase, but not in a non-interacting Anderson insulator. While most of the previously considered probes of dephasing dynamics could be understood by approximating physical spin operators with local integrals of motion, the Loschmidt echo and its generalizations crucially depend on the full expansion of the physical operators via local integrals of motion operators, as well as operators which flip local integrals of motion. Hence, these probes allow to get insights into the relation between physical operators and local integrals of motion, and access the operator spreading in the many-body localized phase.

cond-mat.dis-nn↗

arXiv2016

Superconductivity and Nematic Fluctuations in a model of FeSe monolayers: A Determinant Quantum Monte Carlo Study

In contrast to bulk FeSe, which exhibits nematic order and low temperature superconductivity, atomic layers of FeSe reverse the situation, having high temperature superconductivity appearing alongside a suppression of nematic order. To investigate this phenomenon, we study a minimal electronic model of FeSe, with interactions that enhance nematic fluctuations. This model is sign problem free, and is simulated using determinant quantum Monte Carlo (DQMC). We developed a DQMC algorithm with parallel tempering, which proves to be an efficient source of global updates and allows us to access the region of strong interactions. Over a wide range of intermediate couplings, we observe superconductivity with an extended s-wave order parameter, along with enhanced, but short ranged, $q=(0,0)$ ferro-orbital (nematic) order. These results are consistent with approximate weak coupling treatments that predict that nematic fluctuations lead to superconducting pairing. Surprisingly, in the parameter range under study, we do not observe nematic long range order. Instead, at stronger coupling an unusual insulating phase with $q=(π,π)$ antiferro-orbital order appears, which is missed by weak coupling approximations.

cond-mat.supr-con↗

arXiv2016

Power-Law Entanglement Spectrum in Many-Body Localized Phases

The entanglement spectrum of the reduced density matrix contains information beyond the von Neumann entropy and provides unique insights into exotic orders or critical behavior of quantum systems. Here, we show that strongly disordered systems in the many-body localized phase have power-law entanglement spectra, arising from the presence of extensively many local integrals of motion. The power-law entanglement spectrum distinguishes many-body localized systems from ergodic systems, as well as from ground states of gapped integrable models or free systems in the vicinity of scale-invariant critical points. We confirm our results using large-scale exact diagonalization. In addition, we develop a matrix-product state algorithm which allows us to access the eigenstates of large systems close to the localization transition, and discuss general implications of our results for variational studies of highly excited eigenstates in many-body localized systems.

cond-mat.dis-nn↗

arXiv2016

Thouless energy and multifractality across the many-body localization transition

Thermal and many-body localized phases are separated by a dynamical phase transition of a new kind. We analyze the distribution of off-diagonal matrix elements of local operators across the many-body localization transition (MBLT) in a disordered spin chain, and use it to characterize the breakdown of the eigenstate thermalization hypothesis and to extract the many-body Thouless energy. We find a wide critical region around the MBLT, where Thouless energy becomes smaller than the level spacing, while matrix elements show critical dependence on the energy difference. In the same region, matrix elements, viewed as amplitudes of a fictitious wave function, exhibit strong multifractality. Our findings show that the correlation length becomes larger than the accessible system sizes in a broad range of disorder strength values, and shed light on the critical behaviour of MBL systems.

cond-mat.dis-nn↗

arXiv2016

Thermoelectric transport signatures of Dirac composite fermions in the half-filled Landau level

The half filled Landau level is expected to be approximately particle-hole symmetric, which requires an extension of the Halperin-Lee-Read (HLR) theory of the compressible state observed at this filling. Recent work indicates that, when particle-hole symmetry is preserved, the composite Fermions experience a quantized $π$-Berry phase upon winding around the composite Fermi-surface, analogous to Dirac fermions at the surface of a 3D topological insulator. In contrast, the effective low energy theory of the composite fermion liquid originally proposed by HLR lacks particle-hole symmetry and has vanishing Berry phase. In this paper, we explain how thermoelectric transport measurements can be used to test the Dirac nature of the composite Fermions by quantitatively extracting this Berry phase. First we point out that longitudinal thermopower (Seebeck effect) is non-vanishing due to the unusual nature of particle hole symmetry in this context and is not sensitive to the Berry phase. In contrast, we find that off-diagonal thermopower (Nernst effect) is directly related to the topological structure of the composite Fermi surface, vanishing for zero Berry phase and taking its maximal value for $π$ Berry phase. In contrast, in purely electrical transport signatures the Berry phase contributions appear as small corrections to a large background signal, making the Nernst effect a promising diagnostic of the Dirac nature of composite fermions.

cond-mat.str-el↗

arXiv2016

Landau level splittings, phase transitions, and non-uniform charge distribution in trilayer graphene

We report on magneto-transport studies of dual-gated, Bernal-stacked trilayer graphene (TLG) encapsulated in boron nitride crystals. We observe a quantum Hall effect staircase which indicates a complete lifting of the twelve-fold degeneracy of the zeroth Landau level. As a function of perpendicular electric field, our data exhibits a sequence of phase transitions between all integer quantum Hall states in the filling factor interval $-8<ν<0$. We develop a theoretical model and argue that, in contrast to monolayer and bilayer graphene, the observed Landau level splittings and quantum Hall phase transitions can be understood within a single-particle picture, but imply the presence of a charge density imbalance between the inner and outer layers of TLG, even at charge neutrality and zero transverse electric field. Our results indicate the importance of a previously unaccounted band structure parameter which, together with a more accurate estimate of the other tight-binding parameters, results in a significantly improved determination of the electronic and Landau level structure of TLG.

cond-mat.mes-hall↗

arXiv2015

Spectral statistics across the many-body localization transition

The many-body localization transition (MBLT) between ergodic and many-body localized phase in disordered interacting systems is a subject of much recent interest. Statistics of eigenenergies is known to be a powerful probe of crossovers between ergodic and integrable systems in simpler examples of quantum chaos. We consider the evolution of the spectral statistics across the MBLT, starting with mapping to a Brownian motion process that analytically relates the spectral properties to the statistics of matrix elements. We demonstrate that the flow from Wigner-Dyson to Poisson statistics is a two-stage process. First, fractal enhancement of matrix elements upon approaching the MBLT from the metallic side produces an effective power-law interaction between energy levels, and leads to a plasma model for level statistics. At the second stage, the gas of eigenvalues has local interaction and level statistics belongs to a semi-Poisson universality class. We verify our findings numerically on the XXZ spin chain. We provide a microscopic understanding of the level statistics across the MBLT and discuss implications for the transition that are strong constraints on possible theories.

cond-mat.dis-nn↗

arXiv2015

A criterion for many-body localization-delocalization phase transition

We propose a new approach to probing ergodicity and its breakdown in quantum many-body systems based on their response to a local perturbation. We study the distribution of matrix elements of a local operator between the system's eigenstates, finding a qualitatively different behaviour in the many-body localized (MBL) and ergodic phases. To characterize how strongly a local perturbation modifies the eigenstates, we introduce the parameter ${\cal G}(L)=\langle \ln (V_{nm}/δ) \rangle$, which represents a disorder-averaged ratio of a typical matrix element of a local operator $V$ to the energy level spacing, $δ$; this parameter is reminiscent of the Thouless conductance in the single-particle localization. We show that the parameter ${\cal G}(L)$ decreases with system size $L$ in the MBL phase, and grows in the ergodic phase. We surmise that the delocalization transition occurs when ${\cal G}(L)$ is independent of system size, ${\cal G}(L)={\cal G}_c\sim 1$. We illustrate our approach by studying the many-body localization transition and resolving the many-body mobility edge in a disordered 1D XXZ spin-1/2 chain using exact diagonalization and time-evolving block decimation methods. Our criterion for the MBL transition gives insights into microscopic details of transition. Its direct physical consequences, in particular logarithmically slow transport at the transition, and extensive entanglement entropy of the eigenstates, are consistent with recent renormalization group predictions.

cond-mat.dis-nn↗

arXiv2014

Quantum quenches in the many-body localized phase

Many-body localized (MBL) systems are characterized by the absence of transport and thermalization, and therefore cannot be described by conventional statistical mechanics. In this paper, using analytic arguments and numerical simulations, we study the behaviour of local observables in an isolated MBL system following a quantum quench. For the case of a global quench, we find that the local observables reach stationary, highly non-thermal values at long times as a result of slow dephasing characteristic of the MBL phase. These stationary values retain the local memory of the initial state due to the existence of local integrals of motion in the MBL phase. The temporal fluctuations around stationary values exhibit universal power-law decay in time, with an exponent set by the localization length and the diagonal entropy of the initial state. Such a power-law decay holds for any local observable and is related to the logarithmic in time growth of entanglement in the MBL phase. This behaviour distinguishes the MBL phase from both the Anderson insulator (where no stationary state is reached), and from the ergodic phase (where relaxation is expected to be exponential). For the case of a local quench, we also find a power-law approach of local observables to their stationary values when the system is prepared in a mixed state. Quench protocols considered in this paper can be naturally implemented in systems of ultra cold atoms in disordered optical lattices, and the behaviour of local observables provides a direct experimental signature of many-body localization.

cond-mat.dis-nn↗

arXiv2014

Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators

The tunability of topological surface states (SS) and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In topological crystalline insulators (TCIs), a spontaneously generated Dirac gap was recently observed, which was ascribed to broken cubic crystal symmetry. However, this structural distortion has not been directly observed so far, and the microscopic mechanism of Dirac gap opening via crystal symmetry breaking remains elusive. In this work, we present scanning tunneling microscopy (STM) measurements of a TCI Pb$_{1-x}$Sn$_x$Se for a wide range of alloy compositions spanning the topological and non-topological regimes. STM topographies directly reveal a symmetry-breaking distortion on the surface, which imparts mass to the otherwise massless Dirac electrons - a mechanism analogous to the long sought-after Higgs mechanism in particle physics. Remarkably, our measurements show that the Dirac gap scales with alloy composition, while the magnitude of the distortion remains nearly constant. Based on theoretical calculations, we find the Dirac mass is controlled by the composition-dependent SS penetration depth, which determines the weight of SS in the distorted region that is confined to the surface. Finally, we discover the existence of SS in the non-topological regime, which have the characteristics of gapped, double-branched Dirac fermions.

cond-mat.mes-hall↗

arXiv2014

Symmetry breaking and Landau quantization in topological crystalline insulators

In the recently discovered topological crystalline insulators SnTe and Pb_{1-x}Sn_{x}(Te,Se), crystal symmetry and electronic topology intertwine to create topological surface states with many interesting features including Lifshitz transition, Van-Hove singularity and fermion mass generation. These surface states are protected by mirror symmetry with respect to the (110) plane. In this work we present a comprehensive study of the effects of different mirror-symmetry-breaking perturbations on the (001) surface band structure. Pristine (001) surface states have four branches of Dirac fermions at low-energy. We show that ferroelectric-type structural distortion generates a mass and gaps out some or all of these Dirac points, while strain shifts Dirac points in the Brillouin zone. An in-plane magnetic field leaves surface state gapless, but introduces asymmetry between Dirac points. Finally, an out-of-plane magnetic field leads to discrete Landau levels. We show that the Landau level spectrum has an unusual pattern of degeneracy and interesting features due to the unique underlying band structure. This suggests that Landau level spectroscopy can detect and distinguish between different mechanisms of symmetry breaking in topological crystalline insulators.

cond-mat.mes-hall↗

arXiv2013

Mapping the unconventional orbital texture in topological crystalline insulators

The newly discovered topological crystalline insulators (TCIs) harbor a complex band structure involving multiple Dirac cones. These materials are potentially highly tunable by external electric field, temperature or strain and could find future applications in field-effect transistors, photodetectors, and nano-mechanical systems. Theoretically, it has been predicted that different Dirac cones, offset in energy and momentum-space, might harbor vastly different orbital character, a unique property which if experimentally realized, would present an ideal platform for accomplishing new spintronic devices. However, the orbital texture of the Dirac cones, which is of immense importance in determining a variety of materials properties, still remains elusive in TCIs. Here, we unveil the orbital texture in a prototypical TCI Pb$_{1-x}$Sn$_x$Se. By using Fourier-transform (FT) scanning tunneling spectroscopy (STS) we measure the interference patterns produced by the scattering of surface state electrons. We discover that the intensity and energy dependences of FTs show distinct characteristics, which can directly be attributed to orbital effects. Our experiments reveal the complex band topology involving two Lifshitz transitions and establish the orbital nature of the Dirac bands in this new class of topological materials, which could provide a different pathway towards future quantum applications.

cond-mat.str-el↗

arXiv2013

Local conservation laws and the structure of the many-body localized states

We construct a complete set of local integrals of motion that characterize the many-body localized (MBL) phase. Our approach relies on the assumption that local perturbations act locally on the eigenstates in the MBL phase, which is supported by numerical simulations of the random-field XXZ spin chain. We describe the structure of the eigenstates in the MBL phase and discuss the implications of local conservation laws for its non-equilibrium quantum dynamics. We argue that the many-body localization can be used to protect coherence in the system by suppressing relaxation between eigenstates with different local integrals of motion.

cond-mat.dis-nn↗

arXiv2013

Universal slow growth of entanglement in interacting strongly disordered systems

Recent numerical work by Bardarson et. al. [Phys. Rev. Lett. 109, 017202 (2012)] revealed a slow, logarithmic in time, growth of entanglement entropy for initial product states in a putative many-body localized phase. We show that this surprising phenomenon results from the dephasing due to exponentially small interaction-induced corrections to the eigenenergies of different states. For weak interactions, we find that the entanglement entropy grows as ξln (Vt/\hbar), where V is the interaction strength, and ξis the single-particle localization length. The saturated value of the entanglement entropy at long times is determined by the participation ratios of the initial state over the eigenstates of the subsystem. The proposed mechanism is illustrated with numerical simulations of small systems. Our work shows that the logarithmic entanglement growth is a universal phenomenon characteristic of the many-body localized phase in any number of spatial dimensions, and reveals a broad hierarchy of dephasing time scales present in such a phase.

cond-mat.str-el↗

arXiv2013

Observation of Dirac node formation and mass acquisition in a topological crystalline insulator

In the recently discovered topological crystalline insulators (TCIs), topology and crystal symmetry intertwine to create surface states with a unique set of characteristics. Among the theoretical predictions for TCIs is the possibility of imparting mass to the massless Dirac fermions by breaking crystal symmetry, as well as a Lifshitz transition with a change of Fermi surface topology. Here we report high resolution scanning tunneling microscopy studies of a TCI, Pb1-xSnxSe. We demonstrate the formation of zero mass Dirac fermions protected by crystal symmetry and the mechanism of mass generation via symmetry breaking, which constitute the defining characteristics of TCIs. In addition, we show two distinct regimes of fermiology separated by a Van-Hove singularity at the Lifshitz transition point. Our work paves the way for engineering the Dirac band gap and realizing interaction-driven topological quantum phenomena in TCIs.

cond-mat.mes-hall↗

arXiv2013

Spinon-Phonon Interaction in Algebraic Spin Liquids

Motivated by a search for experimental probes to access the physics of fractionalized excitations called spinons in a spin liquids, we study the interaction of spinons with lattice vibrations. We consider the case of algebraic spin liquid, when spinons have fermionic statistics and a Dirac-like dispersion. We establish the general procedure for deriving spinon-phonon interactions which is based on a symmetry considerations. The procedure is illustrated for four different algebraic spin liquids: pi-flux and staggered-flux phases on a square lattice, pi-flux phase on a kagome lattice, and zero flux phase on a honeycomb lattice. Although the low energy description is similar for all these phases, different underlying symmetry group leads to a distinct form of spinon-phonon interaction Hamiltonian. The explicit form of the spinon-phonon interaction is used to estimate the attenuation of ultrasound in an algebraic spin liquid. The perspectives of the sound attenuation as probe of spinons are discussed.

cond-mat.str-el↗