arXiv subjects

Bela Bauer

Publications and source records attributed to Bela Bauer.

At least 55 records · Page 3Linked to original sources

arXiv2015

Pair Correlations in Doped Hubbard Ladders

Hubbard ladders are an important stepping stone to the physics of the two-dimensional Hubbard model. While many of their properties are accessible to numerical and analytical techniques, the question of whether weakly hole-doped Hubbard ladders are dominated by superconducting or charge-density-wave correlations has so far eluded a definitive answer. In particular, previous numerical simulations of Hubbard ladders have seen a much faster decay of superconducting correlations than expected based on analytical arguments. We revisit this question using a state-of-the-art implementation of the density matrix renormalization group algorithm that allows us to simulate larger system sizes with higher accuracy than before. Performing careful extrapolations of the results, we obtain improved estimates for the Luttinger liquid parameter and the correlation functions at long distances. Our results confirm that, as suggested by analytical considerations, superconducting correlations become dominant in the limit of very small doping.

cond-mat.str-el↗

arXiv2015

Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum

Strongly correlated analogues of topological insulators have been explored in systems with purely on-site symmetries, such as time-reversal or charge conservation. Here, we use recently developed tensor network tools to study a quantum state of interacting bosons which is featureless in the bulk, but distinguished from an atomic insulator in that it exhibits entanglement which is protected by its spatial symmetries. These properties are encoded in a model many-body wavefunction that describes a fully symmetric insulator of bosons on the honeycomb lattice at half filling per site. While the resulting integer unit cell filling allows the state to bypass `no-go' theorems that trigger fractionalization at fractional filling, it nevertheless has nontrivial entanglement, protected by symmetry. We demonstrate this by computing the boundary entanglement spectra, finding a gapless entanglement edge described by a conformal field theory as well as degeneracies protected by the non-trivial action of combined charge-conservation and spatial symmetries on the edge. Here, the tight-binding representation of the space group symmetries plays a particular role in allowing certain entanglement cuts that are not allowed on other lattices of the same symmetry, suggesting that the lattice representation can serve as an additional symmetry ingredient in protecting an interacting topological phase. Our results extend to a related insulating state of electrons, with short-ranged entanglement and no band insulator analogue.

cond-mat.str-el↗

arXiv2015

Universal Gates via Fusion and Measurement Operations on SU$(2)_4$ Anyons

We examine a class of operations for topological quantum computation based on fusing and measuring topological charges for systems with SU$(2)_4$ or $k=4$ Jones-Kauffman anyons. We show that such operations augment the braiding operations, which, by themselves, are not computationally universal. This augmentation results in a computationally universal gate set through the generation of an exact, topologically protected irrational phase gate and an approximate, topologically protected controlled-$Z$ gate.

quant-ph↗

arXiv2015

Spin-orbit physics of j=1/2 Mott insulators on the triangular lattice

The Heisenberg-Kitaev (HK) model on the triangular lattice is conceptually interesting for its interplay of geometric and exchange frustration. HK models are also thought to capture the essential physics of the spin-orbital entanglement in effective $j=1/2$ Mott insulators studied in the context of various 5d transition metal oxides. Here we argue that the recently synthesized Ba$_3$IrTi$_2$O$_9$ is a prime candidate for a microscopic realization of the triangular HK model. We establish that an infinitesimal Kitaev exchange destabilizes the 120$^\circ$ order of the quantum Heisenberg model and results in the formation of an extended $\mathbb{Z}_2$-vortex crystal phase in the parameter regime most likely relevant to the real material. Using a combination of analytical and numerical techniques we map out the entire phase diagram of the model, which further includes various ordered phases as well as an extended nematic phase around the antiferromagnetic Kitaev point.

cond-mat.str-el↗

arXiv2015

Minimizing nonadiabaticities in optical-lattice loading

In the quest to reach lower temperatures of ultra-cold gases in optical lattice experiments, non-adiabaticites during lattice loading are one of the limiting factors that prevent the same low temperatures to be reached as in experiments without lattice. Simulating the loading of a bosonic quantum gas into a one-dimensional optical lattice with and without a trap, we find that the redistribution of atomic density inside a global confining potential is by far the dominant source of heating. Based on these results we propose to adjust the trapping potential during loading to minimize changes to the density distribution. Our simulations confirm that a very simple linear interpolation of the trapping potential during loading already significantly decreases the heating of a quantum gas and we discuss how loading protocols minimizing density redistributions can be designed.

cond-mat.quant-gas↗

arXiv2015

Entanglement as a resource in adiabatic quantum optimization

We explore the role of entanglement in adiabatic quantum optimization by performing approximate simulations of the real-time evolution of a quantum system while limiting the amount of entanglement. To classically simulate the time evolution of the system with a limited amount of entanglement, we represent the quantum state using matrix-product states and projected entangled-pair states. We show that the probability of finding the ground state of an Ising spin glass on either a planar or non-planar two-dimensional graph increases rapidly as the amount of entanglement in the state is increased. Furthermore, we propose evolution in complex time as a way to improve simulated adiabatic evolution and mimic the effects of thermal cooling of the quantum annealer.

cond-mat.dis-nn↗

arXiv2014

Analyzing many-body localization with a quantum computer

Many-body localization, the persistence against electron-electron interactions of the localization of states with non-zero excitation energy density, poses a challenge to current methods of theoretical and numerical analysis. Numerical simulations have so far been limited to a small number of sites, making it difficult to obtain reliable statements about the thermodynamic limit. In this paper, we explore the ways in which a relatively small quantum computer could be leveraged to study many-body localization. We show that, in addition to studying time-evolution, a quantum computer can, in polynomial time, obtain eigenstates at arbitrary energies to sufficient accuracy that localization can be observed. The limitations of quantum measurement, which preclude the possibility of directly obtaining the entanglement entropy, make it difficult to apply some of the definitions of many-body localization used in the recent literature. We discuss alternative tests of localization that can be implemented on a quantum computer.

cond-mat.dis-nn↗

arXiv2014

Matrix Product State applications for the ALPS project

The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as part of the ALPS package, that provide an efficient and flexible implementation of these methods based on a matrix-product state (MPS) representation. Our applications implement, within the same framework, algorithms to variationally find the ground state and low-lying excited states as well as simulate the time evolution of arbitrary one-dimensional and two-dimensional models. Implementing the conservation of quantum numbers for generic Abelian symmetries, we achieve performance competitive with the best codes in the community. Example results are provided for (i) a model of itinerant fermions in one dimension and (ii) a model of quantum magnetism.

cond-mat.str-el↗

arXiv2014

Interplay between Kondo and Majorana interactions in quantum dots

We study the properties of a quantum dot coupled to a one-dimensional topological superconductor and a normal lead and discuss the interplay between Kondo and Majorana-induced couplings in quantum dot. The latter appears due to the presence of Majorana zero-energy modes localized at the ends of the one-dimensional superconductor. We investigate the phase diagram of the system as a function of Kondo and Majorana interactions using a renormalization-group analysis, a slave-boson mean-field theory and numerical simulations using the density-matrix renormalization group method. We show that, in addition to the well-known Kondo fixed point, the system may flow to a new fixed point controlled by the Majorana-induced coupling which is characterized by non-trivial correlations between a localized spin on the dot and the fermion parity of the topological superconductor and normal lead. We compute several measurable quantities such as differential tunneling conductance and impurity spin susceptibility which highlight some peculiar features characteristic to the Majorana fixed point.

cond-mat.mes-hall↗

arXiv2014

Gapped and gapless spin liquid phases on the Kagome lattice from chiral three-spin interactions

We argue that a relatively simple model containing only SU(2)-invariant chiral three-spin interactions on a Kagome lattice of S=1/2 spins can give rise to both a gapped and a gapless quantum spin liquid. Our arguments are rooted in a formulation in terms of network models of edge states and are backed up by a careful numerical analysis. For a uniform choice of chirality on the lattice, we realize the Kalmeyer-Laughlin state, i.e. a gapped spin liquid which is identified as the nu=1/2 bosonic Laughlin state. For staggered chiralities, a gapless spin liquid emerges which exhibits gapless spin excitations along lines in momentum space, a feature that we probe by studying quasi-two-dimensional systems of finite width. We thus provide a single, appealingly simple spin model (i) for what is probably the simplest realization of the Kalmeyer-Laughlin state to date, as well as (ii) for a non-Fermi liquid state with lines of gapless SU(2) spin excitations.

cond-mat.str-el↗

arXiv2014

Helical order in one-dimensional magnetic atom chains and possible emergence of Majorana bound states

We theoretically obtain the phase diagram of localized magnetic impurity spins arranged in a one-dimensional chain on top of a one- or two-dimensional electron gas with Rashba spin-orbit coupling. The interactions between the spins are mediated by the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism through the electron gas. Recent work predicts that such a system may intrinsically support topological superconductivity when a helical spin-density wave is formed in the spins, and superconductivity is induced in the electron gas. We analyze, using both analytical and numerical techniques, the conditions under which such a helical spin state is stable in a realistic situation in the presence of disorder. We show that it becomes unstable towards the formation of (anti) ferromagnetic domains if the disorder in the impurity spin positions $δR$ becomes comparable with the Fermi wave length. We also examine the stability of the helical state against Gaussian potential disorder in the electronic system using a diagrammatic approach. Our results suggest that in order to stabilize the helical spin state, and thus the emergent topological superconductivity, a sufficiently strong Rashba spin-orbit coupling, giving rise to Dzyaloshinskii-Moriya interactions, is required.

cond-mat.mes-hall↗

arXiv2014

Gate count estimates for performing quantum chemistry on small quantum computers

As quantum computing technology improves and quantum computers with a small but non-trivial number of N > 100 qubits appear feasible in the near future the question of possible applications of small quantum computers gains importance. One frequently mentioned application is Feynman's original proposal of simulating quantum systems, and in particular the electronic structure of molecules and materials. In this paper, we analyze the computational requirements for one of the standard algorithms to perform quantum chemistry on a quantum computer. We focus on the quantum resources required to find the ground state of a molecule twice as large as what current classical computers can solve exactly. We find that while such a problem requires about a ten-fold increase in the number of qubits over current technology, the required increase in the number of gates that can be coherently executed is many orders of magnitude larger. This suggests that for quantum computation to become useful for quantum chemistry problems, drastic algorithmic improvements will be needed.

quant-ph↗

arXiv2014

Universality of single quantum gates

We supply a rigorous proof that an open dense set of all possible 2-qubit gates G has the property that if the quantum circuit model is restricted to only permit swap of qubits lines and the application of G to pairs of lines, then the model is still computationally universal.

math.GR↗

arXiv2014

Emergent supersymmetry at the Ising-Berezinskii-Kosterlitz-Thouless multicritical point

We show that supersymmetry emerges in a large class of models in 1+1 dimensions with both Z_2 and U(1) symmetry at the multicritical point where the Ising and Berezinskii-Kosterlitz-Thouless transitions coincide. To arrive at this result we perform a detailed renormalization group analysis of the multicritical theory including all perturbations allowed by symmetry. This analysis reveals an intricate flow with a marginally irrelevant direction that preserves part of the supersymmetry of the fixed point. The slow flow along this special line has significant consequences on the physics of the multicritical point. In particular, we show that the scaling of the U(1) gap away from the multicritical point is different from the usual Berezinskii-Kosterlitz-Thouless exponential gap scaling.

cond-mat.str-el↗

arXiv2013

Area laws in a many-body localized state and its implications for topological order

The question whether Anderson insulators can persist to finite-strength interactions - a scenario dubbed many-body localization - has recently received a great deal of interest. The origin of such a many-body localized phase has been described as localization in Fock space, a picture we examine numerically. We then formulate a precise sense in which a single energy eigenstate of a Hamiltonian can be adiabatically connected to a state of a non-interacting Anderson insulator. We call such a state a many-body localized state and define a many-body localized phase as one in which almost all states are many-body localized states. We explore the possible consequences of this; the most striking is an area law for the entanglement entropy of almost all excited states in a many-body localized phase. We present the results of numerical calculations for a one-dimensional system of spinless fermions. Our results are consistent with an area law and, by implication, many-body localization for almost all states and almost all regions for weak enough interactions and strong disorder. However, there are rare regions and rare states with much larger entanglement entropies. Furthermore, we study the implications that many-body localization may have for topological phases and self-correcting quantum memories. We find that there are scenarios in which many-body localization can help to stabilize topological order at non-zero energy density, and we propose potentially useful criteria to confirm these scenarios.

cond-mat.dis-nn↗

arXiv2013

A supersymmetric multicritical point in a model of lattice fermions

We study a model of spinless fermions with infinite nearest-neighbor repulsion on the square ladder which has microscopic supersymmetry. It has been conjectured that in the continuum the model is described by the superconformal minimal model with central charge c=3/2. Thus far it has not been possible to confirm this conjecture due to strong finite-size corrections in numerical data. We trace the origin of these corrections to the presence of unusual marginal operators that break Lorentz invariance, but preserve part of the supersymmetry. By relying mostly on entanglement entropy calculations with the density-matrix renormalization group, we are able to reduce finite-size effects significantly. This allows us to unambiguously determine the continuum theory of the model. We also study perturbations of the model and establish that the supersymmetric model is a multicritical point. Our work underlines the power of entanglement entropy as a probe of the phases of quantum many-body systems.

cond-mat.str-el↗

arXiv2012

Effect of thermal fluctuations in topological p-wave superconductors

We study the effect of thermal fluctuations on the topological stability of chiral p-wave superconductors. We consider two models of superconductors: spinless and spinful with a focus on topological properties and Majorana zero-energy modes. We show that proliferation of vortex-antivortex pairs above the Kosterlitz-Thouless temperature T_KT drives the transition from a thermal Quantum Hall insulator to a thermal metal/insulator, and dramatically modifies the ground-state degeneracy splitting. Therefore, in order to utilize 2D chiral p-wave superconductors for topological quantum computing, the temperature should be much smaller than T_KT. Within the spinful chiral p-wave model, we also investigate the interplay between half-quantum vortices carrying Majorana zero-energy modes and full-quantum vortices having trivial topological charge, and discuss topological properties of half-quantum vortices in the background of proliferating full-quantum vortices.

cond-mat.supr-con↗

arXiv2012

A new set of generators and a physical interpretation for the SU(3) finite subgroup D(9,1,1;2,1,1)

After 100 years of effort, the classification of all the finite subgroups of SU(3) is yet incomplete. The most recently updated list can be found in P.O. Ludl, J. Phys. A: Math. Theor. 44 255204 (2011), where the structure of the series (C) and (D) of SU(3)-subgroups is studied. We provide a minimal set of generators for one of these groups which has order 162. These generators appear up to phase as the image of an irreducible unitary braid group representation issued from the Jones-Kauffman version of SU(2) Chern-Simons theory at level 4. In light of these new generators, we study the structure of the group in detail and recover the fact that it is isomorphic to the semidirect product Z_9 \times Z_3 \rtimes S_3 with respect to conjugation.

math.GR↗