arXiv subjects

Frank Pollmann

Publications and source records attributed to Frank Pollmann.

At least 163 records · Page 9Linked to original sources

arXiv2018

Quantum spin liquid signatures in Kitaev-like frustrated magnets

Motivated by recent experiments on $α$-RuCl$_3$, we investigate a possible quantum spin liquid ground state of the honeycomb-lattice spin model with bond-dependent interactions. We consider the $K-Γ$ model, where $K$ and $Γ$ represent the Kitaev and symmetric-anisotropic interactions between spin-1/2 moments on the honeycomb lattice. Using the infinite density matrix renormalization group (iDMRG), we provide compelling evidence for the existence of quantum spin liquid phases in an extended region of the phase diagram. In particular, we use transfer matrix spectra to show the evolution of two-particle excitations with well-defined two-dimensional dispersion, which is a strong signature of quantum spin liquid. These results are compared with predictions from Majorana mean-field theory and used to infer the quasiparticle excitation spectra. Further, we compute the dynamical structure factor using finite size cluster computations and show that the results resemble the scattering continuum seen in neutron scattering experiments on $α$-RuCl$_3$. We discuss these results in light of recent and future experiments.

cond-mat.str-el↗

arXiv2018

Topology and edge modes in quantum critical chains

We show that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry protected topological phases. This is possible even without gapped degrees of freedom in the bulk ---in contrast to recent work on edge modes in gapless chains. We present an intuitive picture for the existence of these edge modes in the case of non-interacting spinless fermions with time reversal symmetry (BDI class of the tenfold way). The stability of this phenomenon relies on a topological invariant defined in terms of a complex function, counting its zeros and poles inside the unit circle. This invariant can prevent two models described by the \emph{same} conformal field theory (CFT) from being smoothly connected. A full classification of critical phases in the non-interacting BDI class is obtained: each phase is labeled by the central charge of the CFT, $c \in \frac{1}{2}\mathbb N$, and the topological invariant, $ω\in \mathbb Z$. Moreover, $c$ is determined by the difference in the number of edge modes between the phases neighboring the transition. Numerical simulations show that the topological edge modes of critical chains can be stable in the presence of interactions and disorder.

cond-mat.mes-hall↗

arXiv2017

Quantum thermalization dynamics with Matrix-Product States

We study the dynamics of thermalization following a quantum quench using tensor-network methods. Contrary to the common belief that the rapid growth of entanglement and the resulting exponential growth of the bond dimension restricts simulations to short times, we demonstrate that the long time limit of local observables can be well captured using the time-dependent variational principle. This allows to extract transport coefficients such as the energy diffusion constant from simulations with rather small bond dimensions. We further study the characteristic of the chaotic wave that precedes the emergence of hydrodynamics, to find a ballistic diffusively-broadening wave-front.

cond-mat.stat-mech↗

arXiv2017

Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold atom model

We investigate the fate of hardcore bosons in a Harper-Hofstadter model which was experimentally realized by Aidelsburger et al. [Nature Physics 11 , 162 (2015)] at half filling of the lowest band. We discuss the stability of an emergent fractional Chern insulator (FCI) state in a finite region of the phase diagram that is separated from a superfluid state by a first-order transition when tuning the band topology following the protocol used in the experiment. Since crossing a first-order transition is unfavorable for adiabatically preparing the FCI state, we extend the model to stabilize a featureless insulating state. The transition between this phase and the topological state proves to be continuous, providing a path in parameter space along which an FCI state could be adiabatically prepared. To further corroborate this statement, we perform time-dependent DMRG calculations which demonstrate that the FCI state may indeed be reached by adiabatically tuning a simple product state.

cond-mat.str-el↗

arXiv2017

One-Dimensional Symmetry Protected Topological Phases and their Transitions

We present a unified perspective on symmetry protected topological (SPT) phases in one dimension and address the open question of what characterizes their phase transitions. In the first part of this work we use symmetry as a guide to map various well-known fermionic and spin SPTs to a Kitaev chain with coupling of range $α\in \mathbb Z$. This unified picture uncovers new properties of old models --such as how the cluster state is the fixed point limit of the Affleck-Kennedy-Lieb-Tasaki state in disguise-- and elucidates the connection between fermionic and bosonic phases --with the Hubbard chain interpolating between four Kitaev chains and a spin chain in the Haldane phase. In the second part, we study the topological phase transitions between these models in the presence of interactions. This leads us to conjecture that the critical point between any SPT with $d$-dimensional edge modes and the trivial phase has a central charge $c \geq \log_2 d$. We analytically verify this for many known transitions. This agrees with the intuitive notion that the phase transition is described by a delocalized edge mode, and that the central charge of a conformal field theory is a measure of the gapless degrees of freedom.

cond-mat.str-el↗

arXiv2017

Obtaining highly excited eigenstates of the localized XX chain via DMRG-X

We benchmark a variant of the recently introduced DMRG-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many body localized spin models near a transition.

cond-mat.stat-mech↗

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

Stability of the spin-$1/2$ kagome ground state with breathing anisotropy

We numerically study the spin-$1/2$ breathing kagome lattice. In this variation of the kagome Heisenberg antiferromagnet, the spins belonging to upward and downward facing triangles have different coupling strengths. Using the density matrix renormalization group (DMRG) method and exact diagonalization, we show that the kagome antiferromagnet spin liquid is extremely robust to this anisotropy. Materials featuring this anisotropy -- and especially the recently studied vanadium compound $[{\mathrm{NH}}_{4}{]}_{2}[{\mathbf{C}}_{7}{\mathbf{H}}_{14}\mathbf{N}][{\mathbf{V}}_{7}{\mathbf{O}}_{6}{\mathbf{F}}_{18}]$ (DQVOF) -- may thus be very good candidates to realize the much studied kagome spin liquid. Further, we closely examine the limit of strong breathing anisotropy and find indications of a transition to a nematic phase.

cond-mat.str-el↗

arXiv2017

Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws

Thermalization and scrambling are the subject of much recent study from the perspective of many-body quantum systems with locally bounded Hilbert spaces (`spin chains'), quantum field theory and holography. We tackle this problem in 1D spin-chains evolving under random local unitary circuits and prove a number of exact results on the behavior of out-of-time-ordered commutators (OTOCs), and entanglement growth in this setting. These results follow from the observation that the spreading of operators in random circuits is described by a `hydrodynamical' equation of motion, despite the fact that random unitary circuits do not have locally conserved quantities (e.g., no conserved energy). In this hydrodynamic picture quantum information travels in a front with a `butterfly velocity' $v_{\text{B}}$ that is smaller than the light cone velocity of the system, while the front itself broadens diffusively in time. The OTOC increases sharply after the arrival of the light cone, but we do \emph{not} observe a prolonged exponential regime of the form $\sim e^{λ_\text{L}(t-x/v)}$ for a fixed Lyapunov exponent $λ_\text{L}$. We find that the diffusive broadening of the front has important consequences for entanglement growth, leading to an entanglement velocity that can be significantly smaller than the butterfly velocity. We conjecture that the hydrodynamical description applies to more generic ergodic systems and support this by verifying numerically that the diffusive broadening of the operator wavefront also holds in a more traditional non-random Floquet spin-chain. We also compare our results to Clifford circuits, which have less rich hydrodynamics and consequently trivial OTOC behavior, but which can nevertheless exhibit linear entanglement growth and thermalization.

cond-mat.str-el↗

arXiv2017

Entanglement scaling and spatial correlations of the transverse field Ising model with perturbations

We study numerically the entanglement entropy and spatial correlations of the one dimensional transverse field Ising model with three different perturbations. First, we focus on the out of equilibrium, steady state with an energy current passing through the system. By employing a variety of matrix-product state based methods, we confirm the phase diagram and compute the entanglement entropy. Second, we consider a small perturbation that takes the system away from integrability and calculate the correlations, the central charge and the entanglement entropy. Third, we consider periodically weakened bonds, exploring the phase diagram and entanglement properties first in the situation when the weak and strong bonds alternate (period two-bonds) and then the general situation of a period of n bonds. In the latter case we find a critical weak bond that scales with the transverse field as $J'_c/J$ = $(h/J)^n$, where $J$ is the strength of the strong bond, $J'$ of the weak bond and $h$ the transverse field. We explicitly show that the energy current is not a conserved quantity in this case.

cond-mat.stat-mech↗

arXiv2017

Characterizing time-irreversibility in disordered fermionic systems by the effect of local perturbations

We study the effects of local perturbations on the dynamics of disordered fermionic systems in order to characterize time-irreversibility. We focus on three different systems, the non-interacting Anderson and Aubry-André-Harper (AAH-) models, and the interacting spinless disordered t-V chain. First, we consider the effect on the full many-body wave-functions by measuring the Loschmidt echo (LE). We show that in the extended/ergodic phase the LE decays exponentially fast with time, while in the localized phase the decay is algebraic. We demonstrate that the exponent of the decay of the LE in the localized phase diverges proportionally to the single-particle localization length as we approach the metal-insulator transition in the AAH model. Second, we probe different phases of disordered systems by studying the time expectation value of local observables evolved with two Hamiltonians that differ by a spatially local perturbation. Remarkably, we find that many-body localized systems could lose memory of the initial state in the long-time limit, in contrast to the non-interacting localized phase where some memory is always preserved.

cond-mat.dis-nn↗

arXiv2017

Dynamics of the Kitaev-Heisenberg Model

We introduce a matrix-product state based method to efficiently obtain dynamical response functions for two-dimensional microscopic Hamiltonians, which we apply to different phases of the Kitaev-Heisenberg model. We find significant broad high energy features beyond spin-wave theory even in the ordered phases proximate to spin liquids. This includes the phase with zig-zag order of the type observed in $α$-RuCl$_3$, where we find high energy features like those seen in inelastic neutron scattering experiments. Our results provide an example of a natural path for proximate spin liquid features to arise at high energies above a conventionally ordered state, as the diffuse remnants of spin-wave bands intersect to yield a broad peak at the Brillouin zone center.

cond-mat.str-el↗

arXiv2016

Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model

The antiferromagnetic spin-$1/2$ Heisenberg model on a kagome lattice is one of the most paradigmatic models in the context of spin liquids, yet the precise nature of its ground state is not understood. We use large scale density matrix normalization group simulations (DMRG) on infinitely long cylinders and find indications for the formation of a gapless Dirac spin liquid. First, we use adiabatic flux insertion to demonstrate that the spin gap is much smaller than estimated from previous DMRG simulation. Second, we find that the momentum dependent excitation spectrum, as extracted from the DMRG transfer matrix, exhibits Dirac cones that match those of a $π$-flux free fermion model (the parton mean-field ansatz of a $U(1)$ Dirac spin liquid)

cond-mat.str-el↗

arXiv2016

Domain-wall melting as a probe of many-body localization

Motivated by a recent optical-lattice experiment by Choi et al.[Science 352, 1547 (2016)], we discuss how domain-wall melting can be used to investigate many-body localization. First, by considering noninteracting fermion models, we demonstrate that experimentally accessible measures are sensitive to localization and can thus be used to detect the delocalization-localization transition, including divergences of characteristic length scales. Second, using extensive time-dependent density matrix renormalization group simulations, we study fermions with repulsive interactions on a chain and a two-leg ladder. The extracted critical disorder strengths agree well with the ones found in existing literature.

cond-mat.quant-gas↗

arXiv2016

Distilling momentum-space entanglement in Luttinger liquids at finite temperature

While much is known about the entanglement characteristics of ground states, the properties of reduced thermal density matrices have received significantly less attention. Here we investigate the entanglement content of reduced thermal density matrices for momentum-space bipartitioning in Luttinger liquids using analytical and numerical methods. The low lying part of its spectrum contains an "entanglement gap", which persists up to temperatures comparable to the level spacing. With increasing temperature, the low energy modes acquire dispersion and resemble to those in the physical Hamiltonian with an enhanced effective temperature. The momentum-space entanglement is carried by high energy modes (compared to temperature), featuring a completely flat spectrum. The von-Neumann entropy increases with temperature with a universal Sommerfeld coefficient. The momentum-space entanglement Hamiltonian turns out to be as universal as the physical Hamiltonian.

cond-mat.str-el↗

arXiv2016

Quantum Mutual Information as a Probe for Many-Body Localization

We demonstrate that the quantum mutual information (QMI) is a useful probe to study many-body localization (MBL). First, we focus on the detection of a metal--insulator transition for two different models, the noninteracting Aubry-André-Harper model and the spinless fermionic disordered Hubbard chain. We find that the QMI in the localized phase decays exponentially with the distance between the regions traced out, allowing us to define a correlation length, which converges to the localization length in the case of one particle. Second, we show how the QMI can be used as a dynamical indicator to distinguish an Anderson insulator phase from an MBL phase. By studying the spread of the QMI after a global quench from a random product state, we show that the QMI does not spread in the Anderson insulator phase but grows logarithmically in time in the MBL phase.

cond-mat.str-el↗

arXiv2016

Full counting statistics in the Haldane-Shastry chain

We present analytical and numerical results regarding the magnetization full counting statistics (FCS) of a subsystem in the ground-state of the Haldane-Shastry chain. Exact Pfaffian expressions are derived for the cumulant generating function, as well as any observable diagonal in the spin basis. In the limit of large systems, the scaling of the FCS is found to be in agreement with the Luttinger liquid theory. The same techniques are also applied to inhomogeneous deformations of the chain. This introduces a certain amount of disorder in the system; however we show numerically that this is not sufficient to flow to the random singlet phase, that corresponds to $XXZ$ chains with uncorrelated bond disorder.

cond-mat.str-el↗

arXiv2016

Density-Matrix Renormalization Group study of Many-Body Localization in Floquet Eigenstates

We generalize the recently introduced Density-Matrix Renormalization Group (DMRG-X) [Khemani et al, PRL 2016] algorithm to obtain Floquet eigenstates of one-dimensional, periodically driven many-body localized systems. This generalization is made possible by the fact that the time-evolution operator for a period can be efficiently represented using a matrix-product operator. We first benchmark the method by comparing to exact diagonalization for small systems. We then obtain Floquet eigenstates for larger systems and show unambiguously that the characteristic area-law scaling remains robust.

cond-mat.str-el↗