arXiv subjects

Olexei I. Motrunich

Publications and source records attributed to Olexei I. Motrunich.

At least 55 records · Page 3Linked to original sources

arXiv2015

The half-filled Landau level: the case for Dirac composite fermions

One of the most spectacular experimental findings in the fractional quantum Hall effect is evidence for an emergent Fermi surface when the electron density is nearly half the density of magnetic flux quanta ($ν= 1/2$). The seminal work of Halperin, Lee, and Read (HLR) first predicted that at $ν= 1/2$ composite fermions--bound states of an electron and a pair of vortices--experience zero net magnetic field and can form a "composite Fermi liquid" with an emergent Fermi surface. In this paper we use infinite cylinder DMRG to provide compelling numerical evidence for the existence of a Fermi sea of composite fermions for realistic interactions between electrons at $ν= 1/2$. Moreover, we show that the state is particle-hole symmetric, in contrast to the construction of HLR. Instead, our findings are consistent if the composite fermions are massless Dirac particles, at finite density, similar to the surface state of a 3D topological insulator. Exploiting this analogy we devise a numerical test and successfully observe the suppression of $2k_F$ backscattering characteristic of Dirac particles.

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arXiv2015

A continuous Mott transition between a metal and a quantum spin liquid

More than half a century after first being proposed by Sir Nevill Mott, the deceptively simple question of whether the interaction-driven electronic metal-insulator transition may be continuous remains enigmatic. Recent experiments on two-dimensional materials suggest that when the insulator is a quantum spin liquid, lack of magnetic long-range order on the insulating side may cause the transition to be continuous, or only very weakly first order. Motivated by this, we study a half-filled extended Hubbard model on a triangular lattice strip geometry. We argue, through use of large-scale numerical simulations and analytical bosonization, that this model harbors a continuous (Kosterlitz-Thouless-like) quantum phase transition between a metal and a gapless spin liquid characterized by a spinon Fermi surface, i.e., a "spinon metal." These results may provide a rare insight into the development of Mott criticality in strongly interacting two-dimensional materials and represent one of the first numerical demonstrations of a Mott insulating quantum spin liquid phase in a genuinely electronic microscopic model.

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arXiv2014

Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model

We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions J1 and J2, which possesses a nonmagnetic region that has been debated for many years and might realize the interesting Z2 spin liquid. We use the density matrix renormalization group approach with explicit implementation of SU(2) spin rotation symmetry and study the model accurately on open cylinders with different boundary conditions. With increasing J2, we find a Neel phase, a plaquette valence-bond (PVB) phase with a finite spin gap, and a possible spin liquid in a small region of J2 between these two phases. From the finite-size scaling of the magnetic order parameter, we estimate that the Neel order vanishes at J2/J1~0.44. For 0.5<J2/J1<0.61, we find dimer correlations and PVB textures whose decay lengths grow strongly with increasing system width, consistent with a long-range PVB order in the two-dimensional limit. The dimer-dimer correlations reveal the s-wave character of the PVB order. For 0.44<J2/J1<0.5, spin order, dimer order, and spin gap are small on finite-size systems and appear to scale to zero with increasing system width, which is consistent with a possible gapless SL or a near-critical behavior. We compare and contrast our results with earlier numerical studies.

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arXiv2014

Exact Models for Symmetry-Protected Topological Phases in One Dimension

We present an exactly solvable model for one-dimensional symmetry-protected topological phases with $\mathbb{Z}_N\times\mathbb{Z}_N$ symmetry. The model works by binding point topological defects (domain walls) of one symmetry to charges of the other and condensing these bound states. Binding single topological defects to charges leads to symmetry-protected topological phases, while binding multiple topological defects to charges leads to phases with a combination of symmetry-breaking and topological properties.

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arXiv2014

Model of Fractionalization of Faraday Lines in Compact Electrodynamics

Motivated by ideas of fractionalization and intrinsic topological order in bosonic models with short-range interactions, we consider similar phenomena in formal lattice gauge theory models. Specifically, we show that a compact quantum electrodynamics (CQED) can have, besides the familiar Coulomb and confined phases, additional unusual confined phases where excitations are quantum lines carrying fractions of the elementary unit of electric field strength. We construct a model that has $N$-tupled monopole condensation and realizes $1/N$ fractionalization of the quantum Faraday lines. This phase has another excitation which is a $Z_N$ quantum surface in spatial dimensions five and higher, but can be viewed as a quantum line or a quantum particle in four or three spatial dimensions respectively. These excitation have statistical interactions with the fractionalized Faraday lines; for example, in three spatial dimensions, the particle excitation picks up a Berry phase of $e^{i2π/N}$ when going around the fractionalized Faraday line excitation. We demonstrate the existence of this phase by Monte Carlo simulations in (3+1) space-time dimensions.

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arXiv2013

Phase diagram of spin-1/2 J1-J2 Heisenberg model on honeycomb lattice

We use density matrix renormalization group (DMRG) algorithm to study the phase diagram of the spin-1/2 Heisenberg model on honeycomb lattice with first (J1) and second (J2) neighbor antiferromagnetic interactions, where a Z2 spin liquid region has been proposed. By implementing SU(2) symmetry in the DMRG code, we are able to obtain accurate results for long cylinders with width slightly over 15 lattice spacings and torus up to the size N=2*6*6. With increasing J2, we find a Neel phase with vanishing spin gap and a plaquette valence-bond (PVB) phase with non-zero spin gap. By extrapolating the square of the staggered magnetic moment ms^2 on finite-size cylinders to thermodynamic limit, we find the Neel order vanishing at J2/J1~0.22. For 0.25<J2/J1<0.35, we find a possible PVB order, which shows a fast growing PVB decay length with increasing system width. For 0.22<J2/J1<0.25, both spin and dimer orders are weak for all systems we have studied, which is consistent with a possible spin liquid phase or a deconfined quantum critical point. We present calculations of the topological entanglement entropy, compare the DMRG results with the variational Monte Carlo, and discuss possible scenarios in the thermodynamic limit for this region.

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arXiv2013

Exact realization of Integer and Fractional Quantum Hall Phases in U(1)xU(1) models in (2+1)d

In this work we present a set of microscopic U(1)xU(1) models which realize insulating phases with a quantized Hall conductivity σ_{xy}. The models are defined in terms of physical degrees of freedom, and can be realized by local Hamiltonians. For one set of these models, we find that σ_{xy} is quantized to be an even integer. The origin of this effect is a condensation of objects made up of bosons of one species bound to a single vortex of the other species. For other models, the Hall conductivity can be quantized as a rational number times two. For these systems, the condensed objects contain bosons of one species bound to multiple vortices of the other species. These systems have excitations carrying fractional charges and non-trivial mutual statistics. We present sign-free reformulations of these models which can be studied in Monte Carlo, and we use such reformulations to numerically detect a gapless boundary between the quantum Hall and trivial insulator states. We also present the broader phase diagrams of the models.

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arXiv2013

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau's Fermi-liquid theory is of central importance to many outstanding problems in condensed matter physics. One such problem is that, above the transition temperature and near optimal doping, high-transition-temperature copper-oxide superconductors exhibit `strange metal' behaviour that is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of a strange-metal quantum phase could shed new light on the interesting low-temperature behaviour in the pseudogap regime and on the d-wave superconductor itself. Here we present a theory for a specific example of a strange metal---the 'd-wave metal'. Using variational wavefunctions, gauge theoretic arguments, and ultimately large-scale density matrix renormalization group calculations, we show that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian---the usual t-J model with electron kinetic energy $t$ and two-spin exchange $J$ supplemented with a frustrated electron `ring-exchange' term, which we here examine extensively on the square lattice two-leg ladder. These findings constitute an explicit theoretical example of a genuine non-Fermi-liquid metal existing as the ground state of a realistic model.

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arXiv2012

Monte Carlo Study of a $U(1)\times U(1)$ Loop Model with Modular Invariance

We study a $U(1)\times U(1)$ system in (2+1)-dimensions with long-range interactions and mutual statistics. The model has the same form after the application of operations from the modular group, a property which we call modular invariance. Using the modular invariance of the model, we propose a possible phase diagram. We obtain a sign-free reformulation of the model and study it in Monte Carlo. This study confirms our proposed phase diagram. We use the modular invariance to analytically determine the current-current correlation functions and conductivities in all the phases in the diagram, as well as at special "fixed" points which are unchanged by an operation from the modular group. We numerically determine the order of the phase transitions, and find segments of second-order transitions. For the statistical interaction parameter $θ=π$, these second-order transitions are evidence of a critical loop phase obtained when both loops are trying to condense simulataneously. We also measure the critical exponents of the second-order transitions.

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arXiv2012

Phases and phase transitions in a $U(1)\times U(1)$ system with $θ=2π/3$ mutual statistics

We study a $U(1)\times U(1)$ system with short-range interactions and mutual $θ=2π/3$ statistics in (2+1) dimensions. We are able to reformulate the model to eliminate the sign problem, and perform a Monte Carlo study. We find a phase diagram containing a phase with only small loops and two phases with one species of proliferated loop. We also find a phase where both species of loop condense, but without any gapless modes. Lastly, when the energy cost of loops becomes small we find a phase which is a condensate of bound states, each made up of three particles of one species and a vortex of the other. We define several exact reformulations of the model, which allow us to precisely describe each phase in terms of gapped excitations. We propose field-theoretic descriptions of the phases and phase transitions, which are particularly interesting on the "self-dual" line where both species have identical interactions. We also define irreducible responses useful for describing the phases.

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arXiv2012

Line of continuous phase transitions in a three dimensional U(1) model with 1/r^2 current-current interactions

We study a lattice model of interacting loops in three dimensions with a $1/r^2$ interaction. Using Monte Carlo, we find that the phase diagram contains a line of second-order phase transitions between a phase where the loops are gapped and a phase where they proliferate. The correlation length exponent and critical conductivity vary continuously along this line. Our model is exactly self-dual at a special point on the critical line, which allows us to calculate the critical conductivity exactly at this point.

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arXiv2012

Bose Metals and Insulators on Multi-Leg Ladders with Ring Exchange

We establish compelling evidence for the existence of new quasi-one-dimensional descendants of the d-wave Bose liquid (DBL), an exotic two-dimensional quantum phase of uncondensed itinerant bosons characterized by surfaces of gapless excitations in momentum space [O. I. Motrunich and M. P. A. Fisher, Phys. Rev. B {\bf 75}, 235116 (2007)]. In particular, motivated by a strong-coupling analysis of the gauge theory for the DBL, we study a model of hard-core bosons moving on the $N$-leg square ladder with frustrating four-site ring exchange. Here, we focus on four- and three-leg systems where we have identified two novel phases: a compressible gapless Bose metal on the four-leg ladder and an incompressible gapless Mott insulator on the three-leg ladder. The former is conducting along the ladder and has five gapless modes, one more than the number of legs. This represents a significant step forward in establishing the potential stability of the DBL in two dimensions. The latter, on the other hand, is a fundamentally quasi-one-dimensional phase that is insulating along the ladder but has two gapless modes and incommensurate power law transverse density-density correlations. In both cases, we can understand the nature of the phase using slave-particle-inspired variational wave functions consisting of a product of two distinct Slater determinants, the properties of which compare impressively well to a density matrix renormalization group solution of the model Hamiltonian. Stability arguments are made in favor of both quantum phases by accessing the universal low-energy physics with a bosonization analysis of the appropriate quasi-1D gauge theory. We will briefly discuss the potential relevance of these findings to high-temperature superconductors, cold atomic gases, and frustrated quantum magnets.

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arXiv2012

Majorana Spin Liquids on a two-leg ladder

We realize a gapless Majorana Orbital Liquid (MOL) using orbital degrees of freedom and also an SU(2)-invariant Majorana Spin Liquid (MSL) using both spin and orbital degrees of freedom in Kitaev-type models on a 2-leg ladder. The models are exactly solvable by Kitaev's parton approach, and we obtain long-wavelength descriptions for both Majorana liquids. The MOL has one gapless mode and power law correlations in energy at incommensuare wavevectors, while the SU(2) MSL has three gapless modes and power law correlations in spin, spin-nematic, and local energy observables. We study the stability of such states to perturbations away from the exactly solvable points. We find that both MOL and MSL can be stable against allowed short-range parton interactions. We also argue that both states persist upon allowing $Z_2$ gauge field fluctuations, in that the number of gapless modes is retained, although with an expanded set of contributions to observables compared to the free parton mean field.

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arXiv2011

Monte Carlo Study of a U(1)xU(1) system with π-statistical Interaction

We study a $U(1)\times U(1)$ system with two species of loops with mutual $π$-statistics in (2+1) dimensions. We are able to reformulate the model in a way that can be studied by Monte Carlo and we determine the phase diagram. In addition to a phase with no loops, we find two phases with only one species of loop proliferated. The model has a self-dual line, a segment of which separates these two phases. Everywhere on the segment, we find the transition to be first-order, signifying that the two loop systems behave as immiscible fluids when they are both trying to condense. Moving further along the self-dual line, we find a phase where both loops proliferate, but they are only of even strength, and therefore avoid the statistical interactions. We study another model which does not have this phase, and also find first-order behavior on the self-dual segment.

cond-mat.stat-mech↗

arXiv2011

Sign structures for short-range RVB states on small kagome clusters

We extended the Schwinger boson construction to obtain wave functions that are resonating valence bond (RVB) counterparts of the degenerate coplanar classical states on the Kagome lattice. We examined all 84 of them on the 36-site cluster and found that they form a narrow energy band. On the 12-site cluster, there are only four such states and their superpositions accurately account for the second through fourth exact diagonalization (ED) states, while the ED ground state is accurately reproduced by allowing a particular two-vison insertion on top of the q=0 RVB state. Thus, we have established the RVB sign structures for the low energy states on this cluster.

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arXiv2011

SU(2)-invariant Majorana spin liquid with stable parton Fermi surfaces in an exactly solvable model

We construct an exactly solvable spin-orbital model on a decorated square lattice that realizes an SU(2)-invariant Majorana spin liquid with parton Fermi surfaces, of the kind discussed recently by Biswas et al. [ Phys. Rev. B. {\bf 83}, 245131(2011)]. We find power-law spin correlations as well as power-law spin-nematic correlations with the same dominant $1/|{\bf r}|^3$ envelope. The model is solvable also in the presence of Zeeman magnetic field. One fermion species carries $S^z=0$ quantum number and its Fermi surface is not altered in the field, while the Fermi surfaces of the other species evolve and can disappear. In particular, we find an interesting half-magnetization plateau phase in which spin excitations are gapful while there remain spinless gapless excitations that still produce metal-like thermal properties. In the fully-magnetized phase, the model reduces to the one proposed by Baskaran et al., [arXiv:0908.1614v3] in terms of the orbital degrees of freedom.

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arXiv2011

Spin Bose-Metal and Valence Bond Solid phases in a spin-1/2 model with ring exchanges on a four-leg triangular ladder

We study a spin-1/2 system with Heisenberg plus ring exchanges on a four-leg triangular ladder using the density matrix renormalization group and Gutzwiller variational wave functions. Near an isotropic lattice regime, for moderate to large ring exchanges we find a spin Bose-metal phase with a spinon Fermi sea consisting of three partially filled bands. Going away from the triangular towards the square lattice regime, we find a staggered dimer phase with dimers in the transverse direction, while for small ring exchanges the system is in a featureless rung phase. We also discuss parent states and a possible phase diagram in two dimensions.

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arXiv2011

Power-Law Behavior of Bond Energy Correlators in a Kitaev-type Model with a Stable Parton Fermi Surface

We study bond energy correlation functions in an exactly solvable quantum spin model of Kitaev type on the kagome lattice with stable Fermi surface of partons proposed recently by Chua et al, Ref.\[arXiv:1010.1035]. Even though any spin correlations are ultra-short ranged, we find that the bond energy correlations have power law behavior with a $1/|{\bm r}|^3$ envelope and oscillations at incommensurate wavevectors. We determine the corresponding singular surfaces in momentum space, which provide a gauge-invariant characterization of this gapless spin liquid.

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