arXiv subjects

Olexei I. Motrunich

Publications and source records attributed to Olexei I. Motrunich.

At least 37 records · Page 2Linked to original sources

arXiv2020

New exact eigenstates in the Lesanovsky model, proximity to integrability and the PXP model, and approximate scar states

We study a model of Rydberg atoms in a nearest-neighbor Rydberg blockaded regime, introduced by Lesanovsky in Phys. Rev. Lett. 108, 105301 (2012). This many-body model (which has one parameter $z$) has an exactly known gapped liquid ground state, and two exactly known low-lying excitations. We discover two new exact low-lying eigenstates. We also discuss behavior of the model at small parameter $z$ and its proximity to an integrable model. Lastly, we discuss connections between the Lesanovsky model at intermediate $z$ and so-called PXP model. The PXP model describes a recent experiment that observed unusual revivals from a charge density wave initial state, which are attributed to a set of many-body "scar states" which do not obey the eigenstate thermalization hypothesis. We discuss the possibility of scar states in the Lesanovsky model and present two approximations for them.

cond-mat.quant-gas↗

arXiv2020

Unified structure for exact towers of scar states in the AKLT and other models

Quantum many-body scar states are many-body states with finite energy density in non-integrable models that do not obey the eigenstate thermalization hypothesis. Recent works have revealed "towers" of scar states that are exactly known and are equally spaced in energy, specifically in the AKLT model, the spin-1 XY model, and a spin-1/2 model that conserves number of domain walls. We provide a common framework to understand and prove known exact towers of scars in these systems, by evaluating the commutator of the Hamiltonian and a ladder operator. In particular we provide a simple proof of the scar towers in the integer-spin 1d AKLT models by studying two-site spin projectors. Through this picture we deduce a family of Hamiltonians that share the scar tower with the AKLT model, and also find common parent Hamiltonians for the AKLT and XY model scars. We also introduce new towers of exact states, organized in a "pyramid" structure, in the spin-1/2 model through successive application of a non-local ladder operator.

cond-mat.str-el↗

arXiv2019

Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain: Analogies to deconfined quantum critical points

We study a one-dimensional (1d) system that shows many analogies to proposed two-dimensional (2d) deconfined quantum critical points (DQCP). Our system is a translationally invariant spin-1/2 chain with on-site $Z_2 \times Z_2$ symmetry and time reversal symmetry. It undergoes a direct continuous transition from a ferromagnet (FM), where one of the $Z_2$ symmetries and the time reversal are broken, to a valence bond solid (VBS), where all on-site symmetries are restored while the translation symmetry is broken. The other $Z_2$ symmetry remains unbroken throughout, but its presence is crucial for both the direct transition (via specific Berry phase effect on topological defects, also related to a Lieb-Schultz-Mattis-like theorem) and the precise characterization of the VBS phase (which has crystalline-SPT-like property). The transition has a description in terms of either two domain wall species that "fractionalize" the VBS order parameter or in terms of partons that "fractionalize" the FM order parameter, with each picture having its own $Z_2$ gauge structure. The two descriptions are dual to each other and, at long wavelengths, take the form of a self-dual \emph{gauged} Ashkin-Teller model, reminiscent of the self-dual easy-plane non-compact CP$^1$ model that arises in the description of the 2d easy-plane DQCP. We also find an exact reformulation of the transition that leads to a simple field theory description that explicitly unifies the FM and VBS order parameters; this reformulation can be interpreted as a new parton approach that does not attempt to fractionalize either of the two order parameters but instead encodes them in instantons. Besides providing explicit realizations of many ideas proposed in the context of the 2d DQCP, here in the simpler and fully tractable 1d setting with continuous transition, our study also suggests possible new line of approach to the 2d DQCP.

cond-mat.str-el↗

arXiv2019

Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain

A recent experiment in the Rydberg atom chain observed unusual oscillatory quench dynamics with a charge density wave initial state, and theoretical works identified a set of many-body "scar states" showing nonthermal behavior in the Hamiltonian as potentially responsible for the atypical dynamics. In the same nonintegrable Hamiltonian, we discover several eigenstates at \emph{infinite temperature} that can be represented exactly as matrix product states with finite bond dimension, for both periodic boundary conditions (two exact $E = 0$ states) and open boundary conditions (two $E = 0$ states and one each $E = \pm \sqrt{2}$). This discovery explicitly demonstrates violation of strong eigenstate thermalization hypothesis in this model and uncovers exact quantum many-body scar states. These states show signatures of translational symmetry breaking with period-2 bond-centered pattern, despite being in one dimension at infinite temperature. We show that the nearby many-body scar states can be well approximated as "quasiparticle excitations" on top of our exact $E = 0$ scar states, and propose a quasiparticle explanation of the strong oscillations observed in experiments.

cond-mat.quant-gas↗

arXiv2019

Deconfined quantum critical point in one dimension

We perform a numerical study of a spin-1/2 model with $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry in one dimension which demonstrates an interesting similarity to the physics of two-dimensional deconfined quantum critical points (DQCP). Specifically, we investigate the quantum phase transition between Ising ferromagnetic and valence bond solid (VBS) symmetry-breaking phases. Working directly in the thermodynamic limit using uniform matrix product states, we find evidence for a direct continuous phase transition that lies outside of the Landau-Ginzburg-Wilson paradigm. In our model, the continuous transition is found everywhere on the phase boundary. We find that the magnetic and VBS correlations show very close power law exponents, which is expected from the self-duality of the parton description of this DQCP. Critical exponents vary continuously along the phase boundary in a manner consistent with the predictions of the field theory for this transition. We also find a regime where the phase boundary splits, as suggested by the theory, introducing an intermediate phase of coexisting ferromagnetic and VBS order parameters. Interestingly, we discover a transition involving this coexistence phase which is similar to the DQCP, being also disallowed by Landau-Ginzburg-Wilson symmetry-breaking theory.

cond-mat.str-el↗

arXiv2018

Out-of-time-ordered correlators in short-range and long-range hard-core boson models and in the Luttinger-liquid model

We study out-of-time-ordered correlators (OTOC) in hard-core boson models with short-range and long-range hopping and compare the results to the OTOC in the Luttinger liquid model. For the density operator, a related `commutator function' starts at zero and decays back to zero after the passage of the wavefront in all three models, while the wavefront broadens as $t^{1/3}$ in the short-range model and shows no broadening in the long-range model and the Luttinger liquid model. For the boson creation operator, the corresponding commutator function shows saturation inside the light cone in all three models, with similar wavefront behavior as in the density-density commutator function, despite the presence of a nonlocal string in terms of Jordan-Wigner fermions. For the long-range model and the Luttinger liquid model, the commutator function decays as power law outside the light cone in the long time regime when following different fixed-velocity rays. In all cases, the OTOCs approach their long-time values in a power-law fashion, with different exponents for different observables and short-range vs long-range cases. Our long-range model appears to capture exponents in the Luttinger liquid model (which are found to be independent of the Luttinger parameter in the model). This conclusion also bears on the OTOC calculations in conformal field theories, which we propose correspond to long-ranged models.

cond-mat.str-el↗

arXiv2018

Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian

We numerically assess model wave functions for the recently proposed particle-hole-symmetric Pfaffian (`PH-Pfaffian') topological order, a phase consistent with the recently reported thermal Hall conductance [Banerjee et al., Nature 559, 205 (2018)] at the ever enigmatic $ν=5/2$ quantum-Hall plateau. We find that the most natural Moore-Read-inspired trial state for the PH-Pfaffian, when projected into the lowest Landau level, exhibits a remarkable numerical similarity on accessible system sizes with the corresponding (compressible) composite Fermi liquid. Consequently, this PH-Pfaffian trial state performs reasonably well energetically in the half-filled lowest Landau level, but is likely not a good starting point for understanding the $ν=5/2$ ground state. Our results suggest that the PH-Pfaffian model wave function either encodes anomalously weak $p$-wave pairing of composite fermions or fails to represent a gapped, incompressible phase altogether.

cond-mat.str-el↗

arXiv2018

Out-of-time-ordered correlators in quantum Ising chain

Out-of-time-ordered correlators (OTOC) have been proposed to characterize quantum chaos in generic systems. However, they can also show interesting behavior in integrable models, resembling the OTOC in chaotic systems in some aspects. Here we study the OTOC for different operators in the exactly-solvable one-dimensional quantum Ising spin chain. The OTOC for spin operators that are local in terms of the Jordan-Wigner fermions has a "shell-like" structure: after the wavefront passes, the OTOC approaches its original value in the long-time limit, showing no signature of scrambling; the approach is described by a $t^{-1}$ power law at long time $t$. On the other hand, the OTOC for spin operators that are nonlocal in the Jordan-Wigner fermions has a "ball-like" structure, with its value reaching zero in the long-time limit, looking like a signature of scrambling; the approach to zero, however, is described by a slow power law $t^{-1/4}$ for the Ising model at the critical coupling. These long-time power-law behaviors in the lattice model are not captured by conformal field theory calculations. The mixed OTOC with both local and nonlocal operators in the Jordan-Wigner fermions also has a "ball-like" structure, but the limiting values and the decay behavior appear to be nonuniversal. In all cases, we are not able to define a parametrically large window around the wavefront to extract the Lyapunov exponent.

cond-mat.stat-mech↗

arXiv2018

Implementation of rigorous renormalization group method for ground space and low-energy states of local Hamiltonians

The practical success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad, Landau, Vazirani, and Vidick. The convergence proof, however, relies on "rigorous renormalization group" (RRG) techniques which differ fundamentally from existing algorithms. We introduce an efficient implementation of the theoretical RRG procedure which finds MPS ansatz approximations to the ground spaces and low-lying excited spectra of local Hamiltonians in situations of practical interest. In contrast to other schemes, RRG does not utilize variational methods on tensor networks. Rather, it operates on subsets of the system Hilbert space by constructing approximations to the global ground space in a tree-like manner. We evaluate the algorithm numerically, finding similar performance to DMRG in the case of a gapped nondegenerate Hamiltonian. Even in challenging situations of criticality, or large ground-state degeneracy, or long-range entanglement, RRG remains able to identify candidate states having large overlap with ground and low-energy eigenstates, outperforming DMRG in some cases.

cond-mat.stat-mech↗

arXiv2017

Explicit construction of quasi-conserved local operator of translationally invariant non-integrable quantum spin chain in prethermalization

We numerically construct translationally invariant quasi-conserved operators with maximum range M which best-commute with a non-integrable quantum spin chain Hamiltonian, up to M = 12. In the large coupling limit, we find that the residual norm of the commutator of the quasi-conserved operator decays exponentially with its maximum range M at small M, and turns into a slower decay at larger M. This quasi-conserved operator can be understood as a dressed total "spin-z" operator, by comparing with the perturbative Schrieffer-Wolff construction developed to high order reaching essentially the same maximum range. We also examine the operator inverse participation ratio of the operator, which suggests its localization in the operator Hilbert space. The operator also shows almost exponentially decaying profile at short distance, while the long-distance behavior is not clear due to limitations of our numerical calculation. Further dynamical simulation confirms that the prethermalization-equilibrated values are described by a generalized Gibbs ensemble that includes such quasi-conserved operator.

cond-mat.stat-mech↗

arXiv2017

Lattice realization of a bosonic integer quantum Hall state - trivial insulator transition and relation to the self-dual line in the easy-plane NCCP1 model

We provide an explicit lattice model of bosons with two separately conserved boson species [$U(1)\times U(1)$ global symmetry] realizing a direct transition between an integer quantum Hall effect of bosons and a trivial phase, where any intermediate phase is avoided by an additional symmetry interchanging the two species. If the latter symmetry is absent, we find intermediate superfluid phases where one or the other boson species condenses. We know the precise location of the transition since at this point our model has an exact non-local anti-unitary particle-hole-like symmetry that resembles particle-hole symmetry in the lowest Landau level of electrons. We exactly map the direct transition to our earlier study of the self-dual line of the easy-plane NCCP1 model, in the mathematically equivalent reformulation in terms of two (new) particles with $π$-statistics and identical energetics. While the transition in our model is first-order, we hope that our mappings and recent renewed interest in such self-dual models will stimulate more searches for models with a continuous transition.

cond-mat.str-el↗

arXiv2017

Symmetry and duality in bosonization of two-dimensional Dirac fermions

Recent work on a family of boson-fermion mappings has emphasized the interplay of symmetry and duality: Phases related by a particle-vortex duality of bosons (fermions) are related by time-reversal symmetry in their fermionic (bosonic) formulation. We present exact mappings for a number of concrete models that make this property explicit on the operator level. We illustrate the approach with one- and two-dimensional quantum Ising models, and then similarly explore the duality web of complex bosons and Dirac fermions in (2+1) dimensions.

cond-mat.str-el↗

arXiv2017

Quasiparticle explanation of "weak thermalization" regime under quench in a non-integrable quantum spin chain

Eigenstate Thermalization Hypothesis provides one picture of thermalization in a quantum system by looking at individual eigenstates. However, it is also important to consider how local observables reach equilibrium values dynamically. Quench protocol is one of the settings to study such questions. A recent numerical study [Bañuls, Cirac, and Hastings, Phys. Rev. Lett. 106, 050405 (2011)] of a nonintegrable quantum Ising model with longitudinal field under such quench setting found different behaviors for different initial quantum states. One particular case called "weak thermalization" regime showed apparently persistent oscillations of some observables. Here we provide an explanation of such oscillations. We note that the corresponding initial state has low energy density relative to the ground state of the model. We then use perturbation theory near the ground state and identify the oscillation frequency as essentially a quasiparticle gap. With this quasiparticle picture, we can then address the long-time behavior of the oscillations. Upon making additional approximations which intuitively should only make thermalization weaker, we argue that the oscillations nevertheless decay in the long time limit. As part of our arguments, we also consider a quench from a BEC to a hard-core boson model in one dimension. We find that the expectation value of a single-boson creation operator oscillates but decays exponentially in time, while a pair-boson creation operator has oscillations with a $t^{-3/2}$ decay in time. We also study dependence of the decay time on the density of bosons in the low-density regime and use this to estimate decay time for oscillations in the original spin model.

cond-mat.stat-mech↗

arXiv2016

Entanglement entropy of composite Fermi liquid states on the lattice: In support of the Widom formula

Quantum phases characterized by surfaces of gapless excitations are known to violate the otherwise ubiquitous boundary law of entanglement entropy in the form of a multiplicative log correction: $S\sim L^{d-1} \log L$. Using variational Monte Carlo, we calculate the second Rényi entropy for a model wavefunction of the $ν=1/2$ composite Fermi liquid (CFL) state defined on the two-dimensional triangular lattice. By carefully studying the scaling of the total Rényi entropy and, crucially, its contributions from the modulus and sign of the wavefunction on various finite-size geometries, we argue that the prefactor of the leading $L \log L$ term is equivalent to that in the analogous free fermion wavefunction. In contrast to the recent results of Shao et al. [PRL 114, 206402 (2015)], we thus conclude that the "Widom formula" holds even in this non-Fermi liquid CFL state. More generally, our results further elucidate---and place on a more quantitative footing---the relationship between nontrivial wavefunction sign structure and $S\sim L \log L$ entanglement scaling in such highly entangled gapless phases.

cond-mat.str-el↗

arXiv2016

Vacancy-induced low-energy states in undoped graphene

We demonstrate that a nonzero concentration $n_v$ of static, randomly-placed vacancies in graphene leads to a density $w$ of zero-energy quasiparticle states at the band-center $ε=0$ within a tight-binding description with nearest-neighbour hopping $t$ on the honeycomb lattice. We show that $w$ remains generically nonzero in the compensated case (exactly equal number of vacancies on the two sublattices) even in the presence of hopping disorder, and depends sensitively on $n_v$ and correlations between vacancy positions. For low, {\em but not-too-low} $|ε|/t$ in this compensated case, we show that the density of states (DOS) $ρ(ε)$ exhibits a strong divergence of the form $ρ_{\rm 1D}(ε) \sim |ε|^{-1}/ [\log(t/|ε|)]^{(y+1)} $, which crosses over to the universal low-energy asymptotic form expected on symmetry grounds $ρ_{\rm GW}(ε) \sim |ε|^{-1}e^{-b[\log(t/|ε|)]^{2/3} }$ below a crossover scale $ε_c \ll t$. $ε_c$ is found to decrease rapidly with decreasing $n_v$, while $y$ decreases much more slowly.

cond-mat.str-el↗

arXiv2016

Bosonic Analogue of Dirac Composite Fermi Liquid

We introduce a particle-hole-symmetric metallic state of bosons in a magnetic field at odd-integer filling. This state hosts composite fermions whose energy dispersion features a quadratic band touching and corresponding $2π$ Berry flux protected by particle-hole and discrete rotation symmetries. We also construct an alternative particle-hole symmetric state---distinct in the presence of inversion symmetry---without Berry flux. As in the Dirac composite Fermi liquid introduced by Son, breaking particle-hole symmetry recovers the familiar Chern-Simons theory. We discuss realizations of this phase both in 2D and on bosonic topological insulator surfaces, as well as signatures in experiments and simulations.

cond-mat.str-el↗

arXiv2016

Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions

We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in $(2+1)$ dimensions (QED$_3$) with $N = 1$ fermion flavors. The duality proceeds via an exact, non-local mapping from electrons to dual fermions with long-range interactions encoded by an emergent gauge field. This mapping allows us to construct parent Hamiltonians for exotic topological-insulator surface phases, derive the particle-hole-symmetric field theory of a half-filled Landau level, and nontrivially constrain QED$_3$ scaling dimensions. We similarly establish duality between bosonic topological insulator surfaces and $N = 2$ QED$_3$.

cond-mat.str-el↗

arXiv2015

Monte Carlo study of phase transitions out of Symmetry-Enriched Topological phases of bosons in two dimensions

We study a statistical mechanics model of two species of bosons with mutual statistics $θ=2π/n$ in (2+1) dimensions. This model realizes a fractionalized topological phase of bosons, which is a fractionalized version of the boson integer quantum Hall effect. The model can be studied with sign-free Monte Carlo simulations. We study the phase transitions between the fractionalized topological phase and a trivial insulator, and between different topological phases. We find that these transitions are continuous, and we measure their critical exponents.

cond-mat.stat-mech↗