Thermodynamic behavior of modified integer-spin Kitaev models on the honeycomb lattice.

We study the thermodynamic behavior of modified spin-S Kitaev models introduced by Baskaran, Sen, and Shankar [Phys. Rev. B 78, 115116 (2008)PRBMDO1098-012110.1103/PhysRevB.78.115116]. These models have the property that for half-odd-integer spins their eigenstates map on to those of spin-1/2 Kitaev models, with well-known highly entangled quantum spin-liquid states and Majorana fermions. For integer spins, the Hamiltonian is made out of commuting local operators. Thus, the eigenstates can be chosen to be completely unentangled between different sites, though with a significant degeneracy for each eigenstate. For half-odd-integer spins, the thermodynamic properties can be related to the spin-1/2 Kitaev models apart from an additional degeneracy. Hence we focus here on the case of integer spins. We use transfer matrix methods, high-temperature expansions, and Monte Carlo simulations to study the thermodynamic properties of ferromagnetic and antiferromagnetic models with spin S=1 and S=2. Apart from large residual entropies, which all the models have, we find that they can have a variety of different behaviors. Transfer matrix calculations show that for the different models, the correlation lengths can be finite as T→0, become critical as T→0, or diverge exponentially as T→0. The Z_{2} flux variable associated with each hexagonal plaquette saturates at the value +1 as T→0 in all models except the S=1 antiferromagnet where the mean flux remains zero as T→0. We provide qualitative explanations for these results.

Two Phases Inside the Bose Condensation Dome of Yb_{2}Si_{2}O_{7}.

Recent experimental data on Bose-Einstein condensation of magnons in the spin-gap compound Yb_{2}Si_{2}O_{7} revealed an asymmetric Bose-Einstein condensation dome [G. Hester et al., Phys. Rev. Lett. 123, 027201 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.027201]. We examine modifications to the Heisenberg model on a breathing honeycomb lattice, showing that this physics can be explained by competing anisotropic perturbations. We employ a gamut of analytical and numerical techniques to show that the anisotropy yields a field driven phase transition from a state with broken Ising symmetry to a phase that breaks no symmetries and crosses over to the polarized limit.

Griffiths-McCoy singularities in the dilute transverse-field Ising model: A numerical linked cluster expansion study.

We use numerical linked cluster expansions (NLCEs) to study the site-diluted transverse-field Ising model on the square lattice at T=0. NLCE with a self-consistent mean field on the boundary of the clusters is used to obtain the ground-state magnetization, susceptibility, and structure factor as a function of transverse field h and exchange constant J. Adding site dilution to the model turns NLCE into a series expansion in the dilution parameter p. Studying the divergence of the structure factor allows us to establish the phase diagram in the h/J and p plane. By studying the magnetization of the system in a longitudinal field, we investigate the Griffiths-McCoy singularities. We find that the magnetization develops nonlinearities in the Griffiths phase with exponents that vary continuously with h. Additionally, the probability distribution of the local susceptibility develops long tails in the Griffiths phase, which is studied in terms of its moments.

Quantum Spin Ice with Frustrated Transverse Exchange: From a π-Flux Phase to a Nematic Quantum Spin Liquid.

Quantum spin ice materials, pyrochlore magnets with competing Ising and transverse exchange interactions, have been widely discussed as candidates for a quantum spin-liquid ground state. Here, motivated by quantum chemical calculations for Pr pyrochlores, we present the results of a study for frustrated transverse exchange. Using a combination of variational calculations, exact diagonalization, numerical linked-cluster and series expansions, we find that the previously studied U(1) quantum spin liquid, in its π-flux phase, transforms into a nematic quantum spin liquid at a high-symmetry, SU(2) point.

Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination.

We apply unsupervised machine learning techniques, mainly principal component analysis (PCA), to compare and contrast the phase behavior and phase transitions in several classical spin models-the square- and triangular-lattice Ising models, the Blume-Capel model, a highly degenerate biquadratic-exchange spin-1 Ising (BSI) model, and the two-dimensional XY model-and we examine critically what machine learning is teaching us. We find that quantified principal components from PCA not only allow the exploration of different phases and symmetry-breaking, but they can distinguish phase-transition types and locate critical points. We show that the corresponding weight vectors have a clear physical interpretation, which is particularly interesting in the frustrated models such as the triangular antiferromagnet, where they can point to incipient orders. Unlike the other well-studied models, the properties of the BSI model are less well known. Using both PCA and conventional Monte Carlo analysis, we demonstrate that the BSI model shows an absence of phase transition and macroscopic ground-state degeneracy. The failure to capture the "charge" correlations (vorticity) in the BSI model (XY model) from raw spin configurations points to some of the limitations of PCA. Finally, we employ a nonlinear unsupervised machine learning procedure, the "autoencoder method," and we demonstrate that it too can be trained to capture phase transitions and critical points.

Publisher's Note: Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination [Phys. Rev. E 95, 062122 (2017)].

This corrects the article DOI: 10.1103/PhysRevE.95.062122.

Spin generation via bulk spin current in three-dimensional topological insulators.

To date, spin generation in three-dimensional topological insulators is primarily modelled as a single-surface phenomenon, attributed to the momentum-spin locking on each individual surface. In this article, we propose a mechanism of spin generation where the role of the insulating yet topologically non-trivial bulk becomes explicit: an external electric field creates a transverse pure spin current through the bulk of a three-dimensional topological insulator, which transports spins between the top and bottom surfaces. Under sufficiently high surface disorder, the spin relaxation time can be extended via the Dyakonov-Perel mechanism. Consequently, both the spin generation efficiency and surface conductivity are largely enhanced. Numerical simulation confirms that this spin generation mechanism originates from the unique topological connection of the top and bottom surfaces and is absent in other two-dimensional systems such as graphene, even though they possess a similar Dirac cone-type dispersion.

Nonzero-temperature entanglement negativity of quantum spin models: Area law, linked cluster expansions, and sudden death.

We show that the bipartite logarithmic entanglement negativity (EN) of quantum spin models obeys an area law at all nonzero temperatures. We develop numerical linked cluster (NLC) expansions for the "area-law" logarithmic entanglement negativity as a function of temperature and other parameters. For one-dimensional models the results of NLC are compared with exact diagonalization on finite systems and are found to agree very well. The NLC results are also obtained for two dimensional XXZ and transverse field Ising models. In all cases, we find a sudden onset (or sudden death) of negativity at a finite temperature above which the negativity is zero. We use perturbation theory to develop a physical picture for this sudden onset (or sudden death). The onset of EN or its magnitude are insensitive to classical finite-temperature phase transitions, supporting the argument for absence of any role of quantum mechanics at such transitions. On approach to a quantum critical point at T=0, negativity shows critical scaling in size and temperature.

Early Breakdown of Area-Law Entanglement at the Many-Body Delocalization Transition.

We introduce the numerical linked cluster expansion as a controlled numerical tool for the study of the many-body localization transition in a disordered system with continuous nonperturbative disorder. Our approach works directly in the thermodynamic limit, in any spatial dimension, and does not rely on any finite size scaling procedure. We study the onset of many-body delocalization through the breakdown of area-law entanglement in a generic many-body eigenstate. By looking for initial signs of an instability of the localized phase, we obtain a value for the critical disorder, which we believe should be a lower bound for the true value, that is higher than current best estimates from finite size studies. This implies that most current methods tend to overestimate the extent of the localized phase due to finite size effects making the localized phase appear stable at small length scales. We also study the mobility edge in these systems as a function of energy density, and we find that our conclusion is the same at all examined energies.

Magnetic correlations and pairing in the 1/5-depleted square lattice Hubbard model.

We study the single-orbital Hubbard model on the 1/5-depleted square-lattice geometry, which arises in such diverse systems as the spin-gap magnetic insulator CaV4O9 and ordered-vacancy iron selenides, presenting new issues regarding the origin of both magnetic ordering and superconductivity in these materials. We find a rich phase diagram that includes a plaquette singlet phase, a dimer singlet phase, a Néel and a block-spin antiferromagnetic phase, and stripe phases. Quantum Monte Carlo simulations show that the dominant pairing correlations at half filling change character from d wave in the plaquette phase to extended s wave upon transition to the Néel phase. These findings have intriguing connections to iron-based superconductors, and suggest that some physics of multiorbital systems can be captured by a single-orbital model at different dopings.

Simulated cytoskeletal collapse via tau degradation.

We present a coarse-grained two dimensional mechanical model for the microtubule-tau bundles in neuronal axons in which we remove taus, as can happen in various neurodegenerative conditions such as Alzheimers disease, tauopathies, and chronic traumatic encephalopathy. Our simplified model includes (i) taus modeled as entropic springs between microtubules, (ii) removal of taus from the bundles due to phosphorylation, and (iii) a possible depletion force between microtubules due to these dissociated phosphorylated taus. We equilibrate upon tau removal using steepest descent relaxation. In the absence of the depletion force, the transverse rigidity to radial compression of the bundles falls to zero at about 60% tau occupancy, in agreement with standard percolation theory results. However, with the attractive depletion force, spring removal leads to a first order collapse of the bundles over a wide range of tau occupancies for physiologically realizable conditions. While our simplest calculations assume a constant concentration of microtubule intercalants to mediate the depletion force, including a dependence that is linear in the detached taus yields the same collapse. Applying percolation theory to removal of taus at microtubule tips, which are likely to be the protective sites against dynamic instability, we argue that the microtubule instability can only obtain at low tau occupancy, from 0.06-0.30 depending upon the tau coordination at the microtubule tips. Hence, the collapse we discover is likely to be more robust over a wide range of tau occupancies than the dynamic instability. We suggest in vitro tests of our predicted collapse.

Entanglement in ground and excited states of gapped free-fermion systems and their relationship with Fermi surface and thermodynamic equilibrium properties.

We study bipartite entanglement entropies in the ground and excited states of free-fermion models, where a staggered potential, µs, induces a gap in the spectrum. Ground-state entanglement entropies satisfy the "area law", and the "area-law" coefficient is found to diverge as a logarithm of the staggered potential, when the system has an extended Fermi surface at µs=0. On the square lattice, we show that the coefficient of the logarithmic divergence depends on the Fermi surface geometry and its orientation with respect to the real-space interface between subsystems and is related to the Widom conjecture as enunciated by Gioev and Klich [ Phys. Rev. Lett. 96 100503 (2006)]. For point Fermi surfaces in two-dimension, the "area-law" coefficient stays finite as µs→0. The von Neumann entanglement entropy associated with the excited states follows a "volume law" and allows us to calculate an entropy density function sV(e), which is substantially different from the thermodynamic entropy density function sT(e), when the lattice is bipartitioned into two equal subsystems but approaches the thermodynamic entropy density as the fraction of sites in the larger subsystem, that is integrated out, approaches unity.

Entanglement at a two-dimensional quantum critical point: a numerical linked-cluster expansion study.

We develop a method to calculate the bipartite entanglement entropy of quantum models, in the thermodynamic limit, using a numerical linked-cluster expansion (NLCE) involving only rectangular clusters. It is based on exact diagonalization of all n×m rectangular clusters at the interface between entangled subsystems A and B. We use it to obtain the Renyi entanglement entropy of the two-dimensional transverse field Ising model, for arbitrary real Renyi index α. Extrapolating these results as a function of the order of the calculation, we obtain universal pieces of the entanglement entropy associated with lines and corners at the quantum critical point. They show NLCE to be one of the few methods capable of accurately calculating universal properties of arbitrary Renyi entropies at higher dimensional critical points.

Accuracy of topological entanglement entropy on finite cylinders.

Topological phases are unique states of matter which support nonlocal excitations which behave as particles with fractional statistics. A universal characterization of gapped topological phases is provided by the topological entanglement entropy (TEE). We study the finite size corrections to the TEE by focusing on systems with a Z2 topological ordered state using density-matrix renormalization group and perturbative series expansions. We find that extrapolations of the TEE based on the Renyi entropies with a Renyi index of n≥2 suffer from much larger finite size corrections than do extrapolations based on the von Neumann entropy. In particular, when the circumference of the cylinder is about ten times the correlation length, the TEE obtained using von Neumann entropy has an error of order 10(-3), while for Renyi entropies it can even exceed 40%. We discuss the relevance of these findings to previous and future searches for topological ordered phases, including quantum spin liquids.

Sequence-dependent stability test of a left-handed ß-helix motif.

The left-handed ß-helix (LHBH) is an intriguing, rare structural pattern in polypeptides that has been implicated in the formation of amyloid aggregates. We used accurate all-atom replica-exchange molecular dynamics (REMD) simulations to study the relative stability of diverse sequences in the LHBH conformation. Ensemble-average coordinates from REMD served as a scoring criterion to identify sequences and threadings optimally suited to the LHBH, as in a fold recognition paradigm. We examined the repeatability of our REMD simulations, finding that single simulations can be reliable to a quantifiable extent. We find expected behavior for the positive and negative control cases of a native LHBH and intrinsically disordered sequences, respectively. Polyglutamine and a designed hexapeptide repeat show remarkable affinity for the LHBH motif. A structural model for misfolded murine prion protein was also considered, and showed intermediate stability under the given conditions. Our technique is found to be an effective probe of LHBH stability, and promises to be scalable to broader studies of this and potentially other novel or rare motifs. The superstable character of the designed hexapeptide repeat suggests theoretical and experimental follow-ups.

Finite-temperature critical behavior of mutual information.

We study mutual information for Renyi entropy of arbitrary index n, in interacting quantum systems at finite-temperature critical points, using high-temperature expansion, quantum Monte Carlo simulations and scaling theory. We find that, for n>1, the critical behavior is manifest at two temperatures T(c) and nT(c). For the XXZ model with Ising anisotropy, the coefficient of the area law has a t lnt singularity, whereas the subleading correction from corners has a logarithmic divergence, with a coefficient related to the exact results of Cardy and Peschel. For T

Left handed beta helix models for mammalian prion fibrils.

We propose models for in vitro grown mammalian prion protein fibrils based upon left handed beta helices formed both from the N-terminal and C-terminal regions of the proteinase resistant infectious prion core. The C-terminal threading onto a beta-helical structure is almost uniquely determined by fixing the cysteine disulfide bond on a helix corner. In comparison to known left handed helical peptides, the resulting model structures have similar stability attributes including relatively low root mean square deviations in all atom molecular dynamics, substantial side-chain-to-side-chain hydrogen bonding, good volume packing fraction, and low hydrophilic/hydrophobic frustration. For the N-terminus, we propose a new threading of slightly more than two turns, which improves upon the above characteristics relative to existing three turn beta-helical models. The N-terminal and C-terminal beta helices can be assembled into eight candidate models for the fibril repeat units, held together by large hinge (order 30 residues) domain swapping, with three amenable to fibril promoting domain swapping via a small (five residue) hinge on the N-terminal side. Small concentrations of the metastable C-terminal beta helix in vivo might play a significant role in templating the infectious conformation and in enhancing conversion kinetics for inherited forms of the disease and explain resistance (for canines) involving hypothesized coupling to the methionine 129 sulfur known to play a role in human disease.

Theoretical study of DNA damage recognition via electron transfer from the [4Fe-4S] complex of MutY.

The mechanism of site-specific recognition of DNA by proteins has been a long-standing issue. The DNA glycosylase MutY, for instance, must find the rare 8-oxoguanine-adenine mismatches among the large number of basepairs in the DNA. This protein has a [4Fe-4S] cluster, which is highly conserved in species as diverse as Escherichia Coli and Homo sapiens. The mixed-valent nature of this cluster suggests that charge transfer may play a role in MutY's function. We have studied the energetics of the charge transfer in Bacillus stearothermophilus MutY-DNA complex using multiscale calculation including density functional theory and molecular dynamics. The [4Fe-4S] cluster in MutY is found to undergo 2+ to 3+ oxidation when coupling to DNA through hole transfer, especially when MutY is near an oxoguanine modified base (oxoG). Employing the Marcus theory for electron transfer, we find near optimal Frank-Condon factors for electron transfer from MutY to oxoguanine modified base. MutY has modest selectivity for oxoguanine over guanine due to the difference in oxidation potential. The tunneling matrix element is significantly reduced with the mutation R149W, whereas the mutation L154F reduces the tunneling matrix element as well as the Frank-Condon factor. Both L154F and R149W mutations are known to dramatically reduce or eliminate repair efficiency. We suggest a scenario where the charge transfer leads to a stabilization of the specific binding conformation, which is likely the recognition mode, thus enabling it to find the damaged site efficiently.

Numerical linked-cluster algorithms. I. Spin systems on square, triangular, and kagomé lattices.

We discuss recently introduced numerical linked-cluster (NLC) algorithms that allow one to obtain temperature-dependent properties of quantum lattice models, in the thermodynamic limit, from exact diagonalization of finite clusters. We present studies of thermodynamic observables for spin models on square, triangular, and kagomé lattices. Results for several choices of clusters and extrapolations methods, that accelerate the convergence of NLCs, are presented. We also include a comparison of NLC results with those obtained from exact analytical expressions (where available), high-temperature expansions (HTE), exact diagonalization (ED) of finite periodic systems, and quantum Monte Carlo simulations. For many models and properties NLC results are substantially more accurate than HTE and ED.

Numerical linked-cluster algorithms. II. t-J models on the square lattice.

We discuss the application of a recently introduced numerical linked-cluster (NLC) algorithm to strongly correlated itinerant models. In particular, we present a study of thermodynamic observables: chemical potential, entropy, specific heat, and uniform susceptibility for the t-J model on the square lattice, with Jt=0.5 and 0.3. Our NLC results are compared with those obtained from high-temperature expansions (HTE) and the finite-temperature Lanczos method (FTLM). We show that there is a sizeable window in temperature where NLC results converge without extrapolations whereas HTE diverges. Upon extrapolations, the overall agreement between NLC, HTE, and FTLM is excellent in some cases down to 0.25t . At intermediate temperatures NLC results are better controlled than other methods, making it easier to judge the convergence and numerical accuracy of the method.