arXiv subjects

Frank Pollmann

Publications and source records attributed to Frank Pollmann.

At least 127 records · Page 7Linked to original sources

arXiv2020

Fracton Critical Point in Higher-Order Topological Phase Transition

The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this paper we demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. We present a theory of this quantum critical point (QCP) driven by the fluctuations and percolation of the domain walls between a HOTI and a trivial Mott insulator region. Due to the spinon zero modes that decorate the rough corners of the domain walls, the fluctuations of the phase boundaries trigger a spinon-dipole hopping term with fracton dynamics. Hence we find the QCP is characterized by a critical dipole liquid theory with subsystem $U(1)$ symmetry and the breakdown of the area law entanglement entropy which exhibits a logarithmic enhancement: $L \ln(L)$. Using the density matrix renormalization group (DMRG) method, we analyze the dipole stiffness together with structure factor at the QCP which provide strong evidence of a critical dipole liquid with a Bose surface. These numerical signatures further support the fracton dynamics of the QCP, and suggest a new paradigm for 2D quantum criticality proximate to a topological phase.

cond-mat.str-el↗

arXiv2020

Observing Quasiparticles through the Entanglement Lens

The low energy physics of interacting quantum systems is typically understood through the identification of the relevant quasiparticles or low energy excitations and their quantum numbers. We present a quantum information framework that goes beyond this to examine the nature of the entanglement in the corresponding quantum states. We argue that the salient features of the quasiparticles, including their quantum numbers, locality and fractionalization are reflected in the entanglement spectrum and in the mutual information. We illustrate these ideas in the specific context of the $d=1$ transverse field Ising model with an integrability breaking perturbation.

cond-mat.str-el↗

arXiv2020

Statistical localization: from strong fragmentation to strong edge modes

Certain disorder-free Hamiltonians can be non-ergodic due to a \emph{strong fragmentation} of the Hilbert space into disconnected sectors. Here, we characterize such systems by introducing the notion of `statistically localized integrals of motion' (SLIOM), whose eigenvalues label the connected components of the Hilbert space. SLIOMs are not spatially localized in the operator sense, but appear localized to sub-extensive regions when their expectation value is taken in typical states with a finite density of particles. We illustrate this general concept on several Hamiltonians, both with and without dipole conservation. Furthermore, we demonstrate that there exist perturbations which destroy these integrals of motion in the bulk of the system, while keeping them on the boundary. This results in statistically localized \emph{strong zero modes}, leading to infinitely long-lived edge magnetizations along with a thermalizing bulk, constituting the first example of such strong edge modes in a non-integrable model. We also show that in a particular example, these edge modes lead to the appearance of topological string order in a certain subset of highly excited eigenstates. Some of our suggested models can be realized in Rydberg quantum simulators.

cond-mat.str-el↗

arXiv2020

Entanglement dynamics of a many-body localized system coupled to a bath

The combination of strong disorder and interactions in closed quantum systems can lead to many-body localization (MBL). However this quantum phase is not stable when the system is coupled to a thermal environment. We investigate how MBL is destroyed in systems that are weakly coupled to a dephasive Markovian environment by focusing on their entanglement dynamics. We numerically study the third Rényi negativity $R_3$, a recently proposed entanglement proxy based on the negativity that captures the unbounded logarithmic growth in the closed case and that can be computed efficiently with tensor networks. We also show that the decay of $R_3$ follows a stretched exponential law, similarly to the imbalance, with however a smaller stretching exponent.

cond-mat.str-el↗

arXiv2020

Dissipation-assisted operator evolution method for capturing hydrodynamic transport

We introduce the dissipation-assisted operator evolution (DAOE) method for calculating transport properties of strongly interacting lattice systems in the high temperature regime. DAOE is based on evolving observables in the Heisenberg picture, and applying an artificial dissipation that reduces the weight on non-local operators. We represent the observable as a matrix product operator, and show that the dissipation leads to a decay of operator entanglement, allowing us to capture the dynamics to long times. We test this scheme by calculating spin and energy diffusion constants in a variety of physical models. By gradually weakening the dissipation, we are able to consistently extrapolate our results to the case of zero dissipation, thus estimating the physical diffusion constant with high precision.

cond-mat.str-el↗

arXiv2020

Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians

We show that the combination of charge and dipole conservation---characteristic of fracton systems---leads to an extensive fragmentation of the Hilbert space, which in turn can lead to a breakdown of thermalization. As a concrete example, we investigate the out-of-equilibrium dynamics of one-dimensional spin-1 models that conserve charge (total $S^z$) and its associated dipole moment. First, we consider a minimal model including only three-site terms and find that the infinite temperature auto-correlation saturates to a finite value---showcasing non-thermal behavior. The absence of thermalization is identified as a consequence of the strong fragmentation of the Hilbert space into exponentially many invariant subspaces in the local $S^z$ basis, arising from the interplay of dipole conservation and local interactions. Second, we extend the model by including four-site terms and find that this perturbation leads to a weak fragmentation: the system still has exponentially many invariant subspaces, but they are no longer sufficient to avoid thermalization for typical initial states. More generally, for any finite range of interactions, the system still exhibits non-thermal eigenstates appearing throughout the entire spectrum. We compare our results to charge and dipole moment conserving random unitary circuit models for which we reach identical conclusions.

cond-mat.str-el↗

arXiv2020

Quantum phases of a one-dimensional Majorana-Bose-Hubbard model

Majorana zero modes (MZM-s) occurring at the edges of a 1D, p-wave, spinless superconductor, in absence of fluctuations of the phase of the superconducting order parameter, are quintessential examples of topologically-protected zero-energy modes occurring at the edges of 1D symmetry-protected topological phases. In this work, we numerically investigate the fate of the topological phase in the presence of phase-fluctuations using the density matrix renormalization group (DMRG) technique. To that end, we consider a one-dimensional array of MZM-s on mesoscopic superconducting islands at zero temperature. Cooper-pair and MZM-assisted single-electron tunneling, together with finite charging energy of the mesoscopic islands, give rise to a rich phase-diagram of this model. We show that the system can be in either a Mott-insulating phase, a Luttinger liquid (LL) phase of Cooper-pairs or a second gapless phase. In contrast to the LL of Cooper-pairs, this second phase is characterized by nonlocal string correlation functions which decay algebraically due to gapless charge-$e$ excitations. The three phases are separated from each other by phase-transitions of either Kosterlitz-Thouless or Ising type. Using a Jordan-Wigner transformation, we map the system to a generalized Bose-Hubbard model with two types of hopping and use DMRG to analyze the different phases and the phase-transitions.

cond-mat.mes-hall↗

arXiv2020

Isometric Tensor Network States in Two Dimensions

Tensor network states (TNS) are a promising but numerically challenging tool for simulating two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction of the TNS ansatz that allows for highly efficient contraction of the network. We consider two concrete applications using this ansatz. First, we show that a matrix-product state representation of a 2D quantum state can be iteratively transformed into an isometric 2D TNS. Second, we introduce a 2D version of the time-evolving block decimation algorithm (TEBD$^2$) for approximating the ground state of a Hamiltonian as an isometric TNS, which we demonstrate for the 2D transverse field Ising model.

cond-mat.str-el↗

arXiv2020

Higher-Order Entanglement and Many-Body Invariants for Higher-Order Topological Phases

We discuss how strongly interacting higher-order symmetry protected topological (HOSPT) phases can be characterized from the entanglement perspective: First, we introduce a topological many-body invariant which reveals the non-commutative algebra between flux operator and $C_n$ rotations. We argue that this invariant denotes the angular momentum carried by the instanton which is closely related to the discrete Wen-Zee response and fractional corner charge. Second, we define a new entanglement property, dubbed `higher-order entanglement', to scrutinize and differentiate various higher-order topological phases from a hierarchical sequence of the entanglement structure. We support our claims by numerically studying a super-lattice Bose-Hubbard model that exhibits different HOSPT phases.

cond-mat.str-el↗

arXiv2020

Parton theory of ARPES spectra in anti-ferromagnetic Mott insulators

Angle-resolved photoemission spectroscopy (ARPES) has revealed peculiar properties of mobile dopants in correlated anti-ferromagnets (AFMs). But describing them theoretically, even in simplified toy models, remains a challenge. Here we study ARPES spectra of a single mobile hole in the $t-J$ model. Recent progress in the microscopic description of mobile dopants allows us to use a geometric decoupling of spin and charge fluctuations at strong couplings, from which we conjecture a one-to-one relation of the one-dopant spectral function and the spectrum of a constituting spinon in the \emph{undoped} parent AFM. We thoroughly test this hypothesis for a single hole doped into a 2D Heisenberg AFM by comparing our semi-analytical predictions to previous quantum Monte Carlo results and our large-scale time-dependent matrix product state (td-MPS) calculations of the spectral function. Our conclusion is supported by a microscopic trial wavefuntion describing spinon-chargon bound states, which captures the momentum and $t/J$ dependence of the quasiparticle residue. Our conjecture suggests that ARPES measurements in the pseudogap phase of cuprates can directly reveal the Dirac-fermion nature of the constituting spinons. Specifically, we demonstrate that our trial wavefunction provides a microscopic explanation for the sudden drop of spectral weight around the nodal point associated with the formation of Fermi arcs, assuming that additional frustration suppresses long-range AFM ordering. We benchmark our results by studying the cross-over from two to one dimension, where spinons and chargons are confined and deconfined respectively.

cond-mat.str-el↗

arXiv2019

Simulating quantum many-body dynamics on a current digital quantum computer

Universal quantum computers are potentially an ideal setting for simulating many-body quantum dynamics that is out of reach for classical digital computers. We use state-of-the-art IBM quantum computers to study paradigmatic examples of condensed matter physics -- we simulate the effects of disorder and interactions on quantum particle transport, as well as correlation and entanglement spreading. Our benchmark results show that the quality of the current machines is below what is necessary for quantitatively accurate continuous time dynamics of observables and reachable system sizes are small comparable to exact diagonalization. Despite this, we are successfully able to demonstrate clear qualitative behaviour associated with localization physics and many-body interaction effects.

quant-ph↗

arXiv2019

Fractional corner charges in a 2D super-lattice Bose-Hubbard model

We study a two dimensional super-lattice Bose-Hubbard model with alternating hoppings in the limit of strong on-site interactions. We evaluate the phase diagram of the model around half-filling using the density matrix renormalization group method and find two gapped phases separated by a gapless superfluid region. We demonstrate that the gapped states realize two distinct higher order symmetry protected topological phases, which are protected by a combination of charge conservation and $C_4$ lattice symmetry. The phases are distinguished in terms of a quantized fractional corner charge and a many-body topological invariant that is robust against arbitrary, symmetry preserving edge manipulations. We support our claims by numerically studying the full counting statistics of the corner charge, finding a sharp distribution peaked around the quantized values. These results are experimentally observable in ultracold atomic settings using state of the art quantum gas microscopy.

cond-mat.quant-gas↗

arXiv2019

Matrix product states approaches to operator spreading in ergodic quantum systems

We review different tensor network approaches to study the spreading of operators in generic nonintegrable quantum systems. As a common ground to all methods, we quantify this spreading by means of the Frobenius norm of the commutator of a spreading operator with a local operator, which is usually referred to as the out of time order correlation (OTOC) function. We compare two approaches based on matrix-product states in the Schrödinger picture: the time dependent block decimation (TEBD) and the time dependent variational principle (TDVP), as well as TEBD based on matrix-product operators directly in the Heisenberg picture. The results of all methods are compared to numerically exact results using Krylov space exact time evolution. We find that for the Schrödinger picture the TDVP algorithm performs better than the TEBD algorithm. Moreover the tails of the OTOC are accurately obtained both by TDVP MPS and TEBD MPO. They are in very good agreement with exact results at short times, and appear to be converged in bond dimension even at longer times. However the growth and saturation regimes are not well captured by both methods.

cond-mat.str-el↗

arXiv2019

Dynamics of strongly interacting systems: From Fock-space fragmentation to Many-Body Localization

We study the $t{-}V$ disordered spinless fermionic chain in the strong coupling regime, $t/V\rightarrow 0$. Strong interactions highly hinder the dynamics of the model, fragmenting its Hilbert space into exponentially many blocks in system size. Macroscopically, these blocks can be characterized by the number of new degrees of freedom, which we refer to as movers. We focus on two limiting cases: Blocks with only one mover and the ones with a finite density of movers. The former many-particle block can be exactly mapped to a single-particle Anderson model with correlated disorder in one dimension. As a result, these eigenstates are always localized for any finite amount of disorder. The blocks with a finite density of movers, on the other side, show an MBL transition that is tuned by the disorder strength. Moreover, we provide numerical evidence that its ergodic phase is diffusive at weak disorder. Approaching the MBL transition, we observe sub-diffusive dynamics at finite time scales and find indications that this might be only a transient behavior before crossing over to diffusion.

cond-mat.dis-nn↗

arXiv2019

Isometric Tensor Network representation of string-net liquids

Recently, a class of tensor networks called isometric tensor network states (isoTNS) was proposed which generalizes the canonical form of matrix product states to tensor networks in higher dimensions. While this ansatz allows for efficient numerical computations, it remained unclear which phases admit an isoTNS representation. In this work, we show that two-dimensional string-net liquids, which represent a wide variety of topological phases including discrete gauge theories, admit an exact isoTNS representation. We further show that the isometric form can be preserved after applying a finite depth local quantum circuit. Taken together, these results show that long-range entanglement by itself is not an obstruction to isoTNS representation and suggest that all two-dimensional gapped phases with gappable edges admit an isoTNS representation.

cond-mat.str-el↗

arXiv2019

Sub-ballistic growth of Rényi entropies due to diffusion

We investigate the dynamics of quantum entanglement after a global quench and uncover a qualitative difference between the behavior of the von Neumann entropy and higher Rényi entropies. We argue that the latter generically grow \emph{sub-ballistically}, as $\propto\sqrt{t}$, in systems with diffusive transport. We provide strong evidence for this in both a U$(1)$ symmetric random circuit model and in a paradigmatic non-integrable spin chain, where energy is the sole conserved quantity. We interpret our results as a consequence of local quantum fluctuations in conserved densities, whose behavior is controlled by diffusion, and use the random circuit model to derive an effective description. We also discuss the late-time behavior of the second Rényi entropy and show that it exhibits hydrodynamic tails with \emph{three distinct power laws} occurring for different classes of initial states.

cond-mat.str-el↗

arXiv2019

Entanglement growth after inhomogenous quenches

We study the growth of entanglement in quantum systems with a conserved quantity exhibiting diffusive transport, focusing on how initial inhomogeneities are imprinted on the entropy. We propose a simple effective model, which generalizes the minimal cut picture of \textit{Jonay et al.} in such a way that the `line tension' of the cut depends on the local entropy density. In the case of noisy dynamics, this is described by a Kardar-Parisi-Zhang (KPZ) equation coupled to a diffusing field. We investigate the resulting dynamics and find that initial inhomogeneities of the conserved charge give rise to features in the entanglement profile, whose width and height both grow in time as $\propto\sqrt{t}$. In particular, for a domain wall quench, diffusion restricts entanglement growth to be $S_\text{vN} \lesssim \sqrt{t}$. We find that for charge density wave initial states, these features in the entanglement profile are present even after the charge density has equilibrated. Our conclusions are supported by numerical results on random circuits and deterministic spin chains.

cond-mat.str-el↗

arXiv2019

Solving efficiently the dynamics of many-body localized systems at strong disorder

We introduce a method to efficiently study the dynamical properties of many-body localized systems in the regime of strong disorder and weak interactions. Our method reproduces qualitatively and quantitatively the real-time evolution with a polynomial effort in system size and independent of the desired time scales. We use our method to study quantum information propagation, correlation functions, and temporal fluctuations in one- and two-dimensional MBL systems. Moreover, we outline strategies for a further systematic improvement of the accuracy and we point out relations of our method to recent attempts to simulate the real-time dynamics of quantum many-body systems in classical or artificial neural networks.

cond-mat.dis-nn↗