arXiv subjects

Frank Pollmann

Publications and source records attributed to Frank Pollmann.

At least 199 records · Page 11Linked to original sources

arXiv2015

Variational Monte Carlo simulations using tensor-product projected states

We propose an efficient numerical method, which combines the advantages of recently developed tensor-network based methods and standard trial wave functions, to study the ground state properties of quantum many-body systems. In this approach, we apply a projector in the form of a tensor-product operator to an input wave function, such as a Jastrow-type or Hartree-Fock wave function, and optimize the tensor elements via variational Monte Carlo. The entanglement already contained in the input wave function can considerably reduce the bond dimensions compared to the regular tensor-product state representation. In particular, this allows us to also represent states that do not obey the area law of entanglement entropy. In addition, for fermionic systems, the fermion sign structure can be encoded in the input wave function. We show that the optimized states provide good approximations of the ground-state energy and correlation functions in the cases of two-dimensional bosonic and fermonic systems.

cond-mat.str-el↗

arXiv2015

Distinct trivial phases protected by a point-group symmetry in quantum spin chains

The ground state of the $S=1$ antiferromagnetic Heisenberg chain belongs to the Haldane phase -- a well known example of symmetry-protected topological phase. A staggered field applied to the $S=1$ antiferromagnetic chain breaks all the symmetries that protect the Haldane phase as a topological phase, reducing it to a trivial phase. That is, the Haldane phase is then connected adiabatically to an antiferromagnetic product state. Nevertheless, as long as the symmetry under site-centered inversion combined with a spin rotation is preserved, the phase is still distinct from another trivial phase. We demonstrate the existence of such distinct symmetry-protected trivial phases using a field-theoretical approach and numerical calculations. Furthermore, a general proof and a non-local order parameter are given in terms of an matrix-product state formulation.

cond-mat.str-el↗

arXiv2015

Characterization and stability of a fermionic ν=1/3 fractional Chern insulator

Using the infinite density matrix renormalization group method on an infinite cylinder geometry, we characterize the $1/3$ fractional Chern insulator state in the Haldane honeycomb lattice model at $ν=1/3$ filling of the lowest band and check its stability. We investigate the chiral and topological properties of this state through (i) its Hall conductivity, (ii) the topological entanglement entropy, (iii) the $U(1)$ charge spectral flow of the many body entanglement spectrum, and (iv) the charge of the anyons. In contrast to numerical methods restricted to small finite sizes, the infinite cylinder geometry allows us to access and characterize directly the metal to fractional Chern insulator transition. We find indications it is first order and no evidence of other competing phases. Since our approach does not rely on any band or subspace projection, we are able to prove the stability of the fractional state in the presence of interactions exceeding the band gap, as has been suggested in the literature. As a by-product we discuss the signatures of Chern insulators within this technique.

cond-mat.str-el↗

arXiv2015

Infinite density matrix renormalization group for multicomponent quantum Hall systems

While the simplest quantum Hall plateaus, such as the $ν= 1/3$ state in GaAs, can be conveniently analyzed by assuming only a single active Landau level participates, for many phases the spin, valley, bilayer, subband, or higher Landau level indices play an important role. These `multi-component' problems are difficult to study using exact diagonalization because each component increases the difficulty exponentially. An important example is the plateau at $ν= 5/2$, where scattering into higher Landau levels chooses between the competing non-Abelian Pfaffian and anti-Pfaffian states. We address the methodological issues required to apply the infinite density matrix renormalization group to quantum Hall systems with multiple components and long-range Coulomb interactions, greatly extending accessible system sizes. As an initial application we study the problem of Landau level mixing in the $ν= 5/2$ state. Within the approach to Landau level mixing used here, we find that at the Coulomb point the anti-Pfaffian is preferred over the Pfaffian state over a range of Landau level mixing up to the experimentally relevant values.

cond-mat.str-el↗

arXiv2014

Fragility of Symmetry Protected Topological Order on a Hubbard Ladder

Anfuso and Rosch [Phys. Rev. B 75, 144420 (2007)] showed that the "topological" Haldane phase in a fermionic spin-1/2 ladder can be continuously deformed into a "trivial" phase without explicitly breaking symmetries when local charge fluctuations are taken into account. Within the framework of symmetry protected topological phases, we revisit the model and demonstrate how the Haldane phase can be adiabatically connected to a trivial phase due to charge fluctuations. Furthermore, we show that the Haldane phase remains stable as long as the system is symmetric under particular reflection symmetries.

cond-mat.str-el↗

arXiv2014

Real-time dynamics in the one-dimensional Hubbard model

We consider single-particle properties in the one-dimensional repulsive Hubbard model at commensurate fillings in the metallic phase. We determine the real-time evolution of the retarded Green's function by matrix-product state methods. We find that at sufficiently late times the numerical results are in good agreement with predictions of nonlinear Luttinger liquid theory. We argue that combining the two methods provides a way of determining the single-particle spectral function with very high frequency resolution.

cond-mat.str-el↗

arXiv2014

Many-body localization in a disordered quantum Ising chain

Many-body localization occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. Despite strong evidence for the existence of a many-body localization transition a reliable extraction of the critical disorder strength is difficult due to a large drift with system size in the studied quantities. In this work we explore two entanglement properties that are promising for the study of the manybody localization transition: the variance of the half-chain entanglement entropy of exact eigenstates and the long time change in entanglement after a local quench from an exact eigenstate. We investigate these quantities in a disordered quantum Ising chain and use them to estimate the critical disorder strength and its energy dependence. In addition, we analyze a spin-glass transition at large disorder strength and provide evidence for it being a separate transition. We thereby give numerical support for a recently proposed phase diagram of many-body localization with localization protected quantum order [Huse et al. Phys. Rev. B 88, 014206 (2013)].

cond-mat.str-el↗

arXiv2014

Numerical study of a transition between Z2 topologically ordered phases

Distinguishing different topologically ordered phases and characterizing phase transitions between them is a difficult task due to the absence of local order parameters. In this paper, we use a combination of analytical and numerical approaches to distinguish two such phases and characterize a phase transition between them. The "toric code" and "double semion" models are simple lattice models exhibiting Z2 topological order. Although both models express the same topological ground state degeneracies and entanglement entropies, they are distinct phases of matter because their emergent quasi-particles obey different statistics. For a 1D model, we tune a phase transition between these two phases and obtain an exact solution to the entire phase diagram, finding a second-order Ising x Ising transition. We then use exact diagonalization to study the 2D case and find indications of a first-order transition. We show that the quasi-particle statistics provides a robust indicator of the distinct topological orders throughout the whole phase diagram.

cond-mat.str-el↗

arXiv2014

Interplay of charge and spin fluctuations of strongly interacting electrons on the kagome lattice

We study electrons hopping on a kagome lattice at third filling described by an extended Hubbard Hamiltonian with on-site and nearest-neighbour repulsions in the strongly correlated limit. As a consequence of the commensurate filling and the large interactions, each triangle has precisely two electrons in the effective low energy description, and these electrons form chains of different lengths. The effective Hamiltonian includes the ring exchange around the hexagons as well as the nearest-neighbor Heisenberg interaction. Using large scale exact diagonalization, we find that the effective model exhibits two different phases: If the charge fluctuations are small, the magnetic fluctuations confine the charges to short loops around hexagons, yielding a gapped charge ordered phase. When the charge fluctuations dominate, the system undergoes a quantum phase transition to a resonating plaquette phase with ordered spins and gapless spin excitations. We find that a peculiar conservation law is fulfilled: the electron in the chains can be divided into two sublattices, and this division is conserved by the ring exchange term.

cond-mat.str-el↗

arXiv2014

Double Semion Phase in an Exactly Solvable Quantum Dimer Model on the Kagome Lattice

Quantum dimer models typically arise in various low energy theories like those of frustrated antiferromagnets. We introduce a quantum dimer model on the kagome lattice which stabilizes an alternative $\mathbb{Z}_2$ topological order, namely the so-called "double semion" order. For a particular set of parameters, the model is exactly solvable, allowing us to access the ground state as well as the excited states. We show that the double semion phase is stable over a wide range of parameters using numerical exact diagonalization. Furthermore, we propose a simple microscopic spin Hamiltonian for which the low-energy physics is described by the derived quantum dimer model.

cond-mat.str-el↗

arXiv2014

Time-evolving a matrix product state with long-ranged interactions

We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions are necessary to simulate not just many physical interactions but also higher-dimensional problems with short-ranged interactions. Since our method overcomes the restriction to short-ranged Hamiltonians of most existing methods, it proves particularly useful for studying the dynamics of both power-law interacting one-dimensional systems, such as Coulombic and dipolar systems, and quasi two-dimensional systems, such as strips or cylinders. First, we benchmark the method by verifying a long-standing theoretical prediction for the dynamical correlation functions of the Haldane-Shastry model. Second, we simulate the time evolution of an expanding cloud of particles in the two-dimensional Bose-Hubbard model, a subject of several recent experiments.

cond-mat.str-el↗

arXiv2014

Berry phase induced dimerization in one-dimensional quadrupolar systems

We investigate the effect of the Berry phase on quadrupoles that occur for example in the low-energy description of spin models. Specifically we study here the one-dimensional bilinear-biquadratic spin-one model. An open question for many years about this model is whether it has a non-dimerized fluctuating nematic phase. The dimerization has recently been proposed to be related to Berry phases of the quantum fluctuations. We use an effective low-energy description to calculate the scaling of the dimerization according to this theory, and then verify the predictions using large scale density-matrix renormalization group (DMRG) simulations, giving good evidence that the state is dimerized all the way up to its transition into the ferromagnetic phase. We furthermore discuss the multiplet structure found in the entanglement spectrum of the ground state wave functions.

cond-mat.str-el↗

arXiv2014

Flux insertion, entanglement, and quantized responses

We discuss the construction of a ground state wavefunction on a finite ring given the ground state on a long chain. In the presence of local symmetries, we can obtain the ground state with arbitrary flux inserted through the ring. A key ingredient are the quantum numbers of the entanglement spectrum. This method allows us to characterize phases by measuring quantized responses, such as the Hall conductance, using data contained in the entanglement spectrum. As concrete examples, we show how the Berry phase allows us to map out the phase diagram of a spin-1 model and calculate the Hall conductivity of a quantum Hall system.

cond-mat.str-el↗

arXiv2014

Distinct magnetic phase transition at the surface of an antiferromagnet

In the majority of magnetic systems the surface is required to order at the same temperature as the bulk. In the present study, we report a distinct and unexpected surface magnetic phase transition, uniquely at a lower temperature than the Néel temperature. Employing grazing incidence X-ray resonant magnetic scattering we have observed the near surface behavior of uranium dioxide. UO$_2$ is a non-collinear, triple-q, antiferromagnet with the U ions on an face-centered-cubic lattice. Theoretical investigations establish that at the surface the energy increase, due to the lost bonds, reduces when the spins near the surface rotate, gradually losing their normal to the surface component. At the surface the lowest-energy spin configuration has a double-q (planar) structure. With increasing temperature, thermal fluctuations saturate the in-plane crystal field anisotropy at the surface, leading to soft excitations that have ferromagnetic $XY$ character and are decoupled from the bulk. The structure factor of a finite two-dimensional $XY$ model, fits the experimental data well for several orders of magnitude of the scattered intensity. Our results support a distinct magnetic transition at the surface in the Kosterlitz-Thouless universality class.

cond-mat.str-el↗

arXiv2014

From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model

We consider one-dimensional topological insulators hosting fractionally charged midgap states in the presence and absence of induced superconductivity pairing. Under the protection of a discrete symmetry, relating positive and negative energy states, the solitonic midgap states remain pinned at zero energy when superconducting correlations are induced by proximity effect. When the superconducting pairing dominates the initial insulating gap, Majorana fermion phases develop for a class of insulators. As a concrete example, we study the Creutz model with induced s-wave superconductivity and repulsive Hubbard-type interactions. For a finite wire, without interactions, the solitonic modes originating from the nonsuperconducting model survive at zero energy, revealing a fourfold-degenerate ground state. However, interactions break the aforementioned discrete symmetry and completely remove this degeneracy, thereby producing a unique ground state which ischaracterized by a topological bulk invariant with respect to the product of fermion parity and bond inversion. In contrast, the Majorana edge modes are globally robust to interactions. Moreover, the parameter range for which a topological Majorana phase is stabilized expands when increasing the repulsive Hubbard interaction. The topological phase diagram of the interacting model is obtained using a combination of mean-field theory and density matrix renormalization group techniques.

cond-mat.mes-hall↗

arXiv2013

Detection of Symmetry Enriched Topological Phases

Topologically ordered systems in the presence of symmetries can exhibit new structures which are referred to as symmetry enriched topological (SET) phases. We introduce simple methods to detect the SET order directly from a complete set of topologically degenerate ground state wave functions. In particular, we first show how to directly determine the characteristic symmetry fractionalization of the quasiparticles from the reduced density matrix of the minimally entangled states. Second, we show how a simple generalization of a non-local order parameter can be measured to detect SETs. The usefulness of the proposed approached is demonstrated by examining two concrete model states which exhibit SET: (i) a spin-1 model on the honeycomb lattice and (ii) the resonating valence bond state on a kagome lattice. We conclude that the spin-1 model and the RVB state are in the same SET phases.

cond-mat.str-el↗

arXiv2013

Coulombic Charge Ice

We consider a classical model of charges $\pm q$ on a pyrochlore lattice in the presence of long range Coulomb interactions. This model first appeared in the early literature on charge order in magnetite. In the limit where the interactions become short-ranged, the model has a ground state with an extensive entropy and dipolar charge-charge correlations. When long range interactions are introduced, the exact degeneracy is broken. We study the thermodynamics of the model and show the presence of a correlated charge liquid within a temperature window in which the physics is well described as a liquid of screened charged defects. The structure factor in this phase, which has smeared pinch points at the reciprocal lattice points, may be used to detect charge ice experimentally. In addition, the model exhibits fractionally charged excitations $\pm q/2$ which are shown to interact via a $1/r$ potential. At lower temperatures, the model exhibits a transition to a long-range ordered phase. We are able to treat the Coulombic charge ice model and the dipolar spin ice model on an equal footing by mapping both to a constrained charge model on the diamond lattice. We find that states of the two ice models are related by a staggering field which is reflected in the energetics of these two models. From this perspective we can understand the origin of the spin ice and charge ice ground states as coming from a dipolar model on a diamond lattice. We study the properties of charge ice in an external electric field finding that the correlated liquid is robust to the presence of a field in contrast to the case of spin ice in a magnetic field. Finally, we comment on the transport properties of Coulombic charge ice in the correlated liquid phase.

cond-mat.str-el↗

arXiv2013

Topological phases in gapped edges of fractionalized systems

Recently, it has been proposed that exotic one-dimensional phases can be realized by gapping out the edge states of a fractional topological insulator. The low-energy edge degrees of freedom are described by a chain of coupled parafermions. We introduce a classification scheme for the phases that can occur in parafermionic chains. We find that the parafermions support both topological symmetry fractionalized phases as well as phases in which the parafermions condense. In the presence of additional symmetries, the phases form a non-Abelian group. As a concrete example of the classification, we consider the effective edge model for a $ν= 1/3$ fractional topological insulator for which we calculate the entanglement spectra numerically and show that all possible predicted phases can be realized.

cond-mat.str-el↗