arXiv subjects

Sergei V. Isakov

Publications and source records attributed to Sergei V. Isakov.

47 records · Page 3Linked to original sources

arXiv2011

Néel to dimer transition in spin-S antiferromagnets: Comparing bond operator theory with quantum Monte Carlo simulations for bilayer Heisenberg models

We study the Néel to dimer transition driven by interlayer exchange coupling in spin-S Heisenberg antiferromagnets on bilayer square and honeycomb lattices for S=1/2, 1, 3/2. Using exact stochastic series expansion quantum Monte Carlo (QMC) calculations, we find that the critical value of the interlayer coupling, J_{\perp c}[S], increases with increasing S, with clear evidence that the transition is in the O(3) universality class for all S. Using bond operator mean field theory restricted to singlet and triplet states, we find J_{\perp c}[S] ~ S(S+1), in qualitative accord with QMC, but the resulting J_{\perp c} [S] is significantly smaller than the QMC value. For S=1/2, incorporating triplet-triplet interactions within a variational approach yields a critical interlayer coupling which agrees well with QMC. For higher spin, we argue that it is crucial to account for the high energy quintet modes, and show that including these within a perturbative scheme leads to reasonable agreement with QMC results for S=1,3/2. We discuss the broad implications of our results for systems such as the triangular lattice S=1 dimer compound Ba_3Mn_2O_8 and the S=3/2 bilayer honeycomb material Bi_3Mn_4O_{12}(NO_{3}).

cond-mat.other↗

arXiv2011

Universal Signatures of Fractionalized Quantum Critical Points

Groundstates of certain materials can support exotic excitations with a charge that's a fraction of the fundamental electron charge. The condensation of these fractionalized particles has been predicted to drive novel quantum phase transitions, which haven't yet been observed in realistic systems. Through numerical and theoretical analysis of a physical model of interacting lattice bosons, we establish the existence of such an exotic critical point, called XY*. We measure a highly non-classical critical exponent eta = 1.49(2), and construct a universal scaling function of winding number distributions that directly demonstrates the distinct topological sectors of an emergent Z_2 gauge field. The universal quantities used to establish this exotic transition can be used to detect other fractionalized quantum critical points in future model and material systems.

cond-mat.str-el↗

arXiv2011

Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid

The Landau paradigm of classifying phases by broken symmetries was demonstrated to be incomplete when it was realized that different quantum Hall states could only be distinguished by more subtle, topological properties. Today, the role of topology as an underlying description of order has branched out to include topological band insulators, and certain featureless gapped Mott insulators with a topological degeneracy in the groundstate wavefunction. Despite intense focus, very few candidates for these topologically ordered "spin liquids" exist. The main difficulty in finding systems that harbour spin liquid states is the very fact that they violate the Landau paradigm, making conventional order parameters non-existent. Here, we uncover a spin liquid phase in a Bose-Hubbard model on the kagome lattice, and measure its topological order directly via the topological entanglement entropy. This is the first smoking-gun demonstration of a non-trivial spin liquid, identified through its entanglement entropy as a gapped groundstate with emergent Z2 gauge symmetry.

cond-mat.str-el↗

arXiv2011

Topological Phases: An Expedition off Lattice

Motivated by the goal to give the simplest possible microscopic foundation for a broad class of topological phases, we study quantum mechanical lattice models where the topology of the lattice is one of the dynamical variables. However, a fluctuating geometry can remove the separation between the system size and the range of local interactions, which is important for topological protection and ultimately the stability of a topological phase. In particular, it can open the door to a pathology, which has been studied in the context of quantum gravity and goes by the name of `baby universe', Here we discuss three distinct approaches to suppressing these pathological fluctuations. We complement this discussion by applying Cheeger's theory relating the geometry of manifolds to their vibrational modes to study the spectra of Hamiltonians. In particular, we present a detailed study of the statistical properties of loop gas and string net models on fluctuating lattices, both analytically and numerically.

cond-mat.stat-mech↗

arXiv2009

Bose-Hubbard model on a star lattice

We analyze the Bose-Hubbard model of hardcore bosons with nearest neighbor hopping and repulsive interactions on a star lattice using both quantum Monte Carlo simulation and dual vortex theory. We obtain the phase diagram of this model as a function of the chemical potential and the relative strength of hopping and interaction. In the strong interaction regime, we find that the Mott phases of the model at 1/2 and 1/3 fillings, in contrast to their counterparts on square, triangular, and Kagome lattices, are either translationally invariant resonant valence bond (RVB) phases with no density-wave order or have coexisting density-wave and RVB orders. We also find that upon increasing the relative strength of hopping and interaction, the translationally invariant Mott states undergo direct second order superfluid-insulator quantum phase transitions. We compute the critical exponents for these transitions and argue using the dual vortex picture that the transitions, when approached through the tip of the Mott lobe, belong to the inverted XY universality class.

cond-mat.str-el↗

arXiv2009

Commensurate lock-in and incommensurate supersolid phases of hardcore bosons on anisotropic triangular lattices

We investigate the interplay between commensurate lock-in and incommensurate supersolid phases of the hardcore bosons at half-filling with anisotropic nearest-neighbor hopping and repulsive interactions on triangular lattice. We use numerical quantum and variational Monte Carlo as well as analytical Schwinger boson mean-field analysis to establish the ground states and phase diagram. It is shown that, for finite size systems, there exist a series of jumps between different supersolid phases as the anisotropy parameter is changed. The density ordering wavevectors are locked to commensurate values and jump between adjacent supersolids. In the thermodynamic limit, however, the magnitude of these jumps vanishes leading to a continuous set of novel incommensurate supersoild phases.

cond-mat.str-el↗

arXiv2008

Fate of partial order on the trillium and distorted windmill lattices

The classical Heisenberg model on the trillium and distorted windmill lattices exhibits a degenerate ground state within large-$N$ theory, where the degenerate wavevectors form a surface and line, in 3-dimensional space, respectively. We name such states partially ordered to represent the existence of long-range order along the direction normal to these degenerate manifolds. We investigate the effects of thermal fluctuations using Monte Carlo (MC) methods, and find a first order transition to a magnetically ordered state for both cases. We further show that the ordering on the distorted windmill lattice is due to order by disorder, while the ground state of the trillium lattice is unique. Despite these different routes to the realization of low temperature ordered phases, the static structure factors obtained by large-$N$ theory and MC simulations for each lattice show quantitative agreement in the cooperative paramagnetic regime at finite temperatures. This suggests that a remnant of the characteristic angle-dependent spin correlations of partial order remains above the transition temperatures for both lattices. The possible relevance of these results to $β$-Mn, CeIrSi, and MnSi is discussed.

cond-mat.str-el↗

arXiv2008

Quantum order by disorder in a spin-one frustrated magnet on the kagome lattice

We study the XXZ spin-one quantum magnet on the kagome lattice as an example where quantum fluctuations on highly degenerate classical ground states lead to various exotic quantum ground states. Previous studies have predicted several quantum phases, but different analytical approaches do not necessarily lead to the same physical picture. In this work, we use Quantum Monte Carlo computations to critically examine some of the predictions made in the string-net mean-field theory and the degenerate perturbation theory combined with duality analysis and effective field theory. It is found that the resulting phase diagram differs from some of the previous predictions. Further implications of our results to different analytical approaches are discussed.

cond-mat.str-el↗

arXiv2008

Unusual liquid state of hard-core bosons on the pyrochlore lattice

We study the physics of hard-core bosons with unfrustrated hopping (t) and nearest-neighbor repulsion (V) on the three dimensional pyrochlore lattice. At half-filling, we demonstrate that the small V/t superfluid state eventually becomes unstable at large enough V/t to an unusual insulating state which displays no broken lattice translation symmetry. Equal time and static density correlators in this insulator are well described by a mapping to electric field correlators in the Coulomb phase of a U(1) lattice gauge theory, allowing us to identify this insulator with a U(1) fractionalized Mott-insulating state. The possibility of observing this phase in suitably designed atom-trap experiments with ultracold atoms is also discussed, as are specific experimental signatures.

cond-mat.str-el↗

arXiv2007

Classical antiferromagnet on a hyperkagome lattice

Motivated by recent experiments on Na_4Ir_3O_8 [Y. Okamoto, M. Nohara, H. Aruga-Katori, and H. Takagi, arXiv:0705.2821 (unpublished)], we study the classical antiferromagnet on a frustrated three-dimensional lattice obtained by selectively removing one of four sites in each tetrahedron of the pyrochlore lattice. This ``hyperkagome'' lattice consists of corner-sharing triangles. We present the results of large-N mean field theory and Monte Carlo computations on O(N) classical spin models. It is found that the classical ground states are highly degenerate. Nonetheless a nematic order emerges at low temperatures in the Heisenberg model (N=3) via ``order by disorder'', representing the dominance of coplanar spin configurations. Implications for ongoing experiments are discussed.

cond-mat.stat-mech↗

arXiv2007

Exotic phase diagram of a cluster charging model of bosons on the kagome lattice

We study a model of hard-core bosons on the kagome lattice with short-range hopping ($t$) and repulsive interactions ($V$). This model directly maps on to an easy-axis $S=1/2$ XXZ model on the kagome lattice and is also related, at large $V/t$, to a quantum dimer model on the triangular lattice. Using quantum Monte Carlo (QMC) numerics, we map out the phase diagram of this model at half-filling. At T=0, we show that this model exhibits a superfluid phase at small $V/t$ and an insulating phase at large $V/t$, separated by a continuous quantum phase transition at $V_c/t \approx 19.8$. The insulating phase at T=0 appears to have no conventional broken symmetries, and is thus a uniform Mott insulator (a `spin liquid' in magnetic language). We characterize this insulating phase as a uniform $Z_2$ fractionalized insulator from the topological order in the ground state and estimate its vison gap. Consistent with this identification, there is no apparent thermal phase transition upon heating the insulator. The insulating phase instead smoothly crosses over into the high temperature paramagnet via an intermediate cooperative paramagnetic regime. We also study the superfluid-to-normal thermal transition for $V < V_c$. We find that this is a Kosterlitz-Thouless transition at small $V/t$ but changes to a first order transition for $V$ closer to $V_c$. We argue that this first order thermal transition is consistent with the presence of a nearby $Z_2$ insulating ground state obtained from the superfluid ground state by condensing double vortices.

cond-mat.str-el↗