arXiv subjects

Abhishodh Prakash

Publications and source records attributed to Abhishodh Prakash.

At least 37 records · Page 2Linked to original sources

arXiv2023

Long-ranged spectral correlations in eigenstate phases

We study non-local measures of spectral correlations and their utility in characterizing and distinguishing between the distinct eigenstate phases of quantum chaotic and many-body localized systems. We focus on two related quantities, the spectral form factor and the density of all spectral gaps, and show that they furnish unique signatures that can be used to sharply identify the two phases. We demonstrate this by numerically studying three one-dimensional quantum spin chain models with (i) quenched disorder, (ii) periodic drive (Floquet), and (iii) quasiperiodic detuning. We also clarify in what ways the signatures are universal and in what ways they are not. More generally, this thorough analysis is expected to play a useful role in classifying phases of disorder systems.

cond-mat.dis-nn↗

arXiv2023

Multiversality and Unnecessary Criticality in One Dimension

We present microscopic models of spin ladders which exhibit continuous critical surfaces whose properties and existence, unusually, cannot be inferred from those of the flanking phases. These models exhibit either `multiversality' -- the presence of different universality classes over finite regions of a critical surface separating two distinct phases -- or its close cousin, `unnecessary criticality'-- the presence of a stable critical surface within a single, possibly trivial, phase. We elucidate these properties using Abelian bosonization and density-matrix renormalization-group simulations, and attempt to distill the key ingredients required to generalize these considerations.

cond-mat.str-el↗

arXiv2021

Boundary supersymmetry of 1+1 d fermionic SPT phases

We prove that the boundaries of all non-trivial 1+1 dimensional intrinsically fermionic symmetry-protected-topological phases, protected by finite on-site symmetries (unitary or anti-unitary), are supersymmetric quantum mechanical systems. This supersymmetry does not require any fine-tuning of the underlying Hamiltonian, arises entirely as a consequence of the boundary 't Hooft anomaly that classifies the phase and is related to a `Bose-Fermi' degeneracy different in nature from other well known degeneracies such as Kramers doublets.

cond-mat.str-el↗

arXiv2021

Universal spectral form factor for many-body localization

We theoretically study correlations present deep in the spectrum of many-body-localized systems. An exact analytical expression for the spectral form factor of Poisson spectra can be obtained and is shown to agree well with numerical results on two models exhibiting many-body-localization: a disordered quantum spin chain and a phenomenological $l$-bit model based on the existence of local integrals of motion. We also identify a universal regime that is insensitive to the global density of states as well as spectral edge effects.

cond-mat.dis-nn↗

arXiv2020

Unwinding Fermionic SPT Phases: Supersymmetry Extension

We show how 1+1-dimensional fermionic symmetry-protected topological states (SPTs, i.e. nontrivial short-range entangled gapped phases of quantum matter whose boundary exhibits 't Hooft anomaly and whose bulk cannot be deformed into a trivial tensor product state under finite-depth local unitary transformations only in the presence of global symmetries), indeed can be unwound to a trivial state by enlarging the Hilbert space via adding extra degrees of freedom and suitably extending the global symmetries. The extended projective global symmetry on the boundary can become supersymmetric in a specific sense, i.e., it contains group elements that do not commute with the fermion number parity $(-1)^F$, while the anti-unitary time-reversal symmetry becomes fractionalized. This also means we can uplift and remove certain exotic fermionic anomalies (e.g., "parity" anomaly in time-reversal or reflection symmetry) via appropriate supersymmetry extensions in terms of group extensions. We work out explicit examples for multi-layers of 1+1d Majorana fermion chains, then comment on models with Sachdev-Ye-Kitaev (SYK) interactions, intrinsic fermionic gapless SPTs protected by supersymmetry, and generalizations to higher spacetime dimensions via a cobordism theory.

cond-mat.str-el↗

arXiv2020

An elementary proof of 1D LSM theorems

The Lieb-Schultz-Mattis (LSM) theorem and its generalizations forbids the existence of a unique gapped ground state in the presence of certain lattice and internal symmetries and thus imposes powerful constraints on the low energy properties of quantum many-body systems. We provide an elementary proof of a class of generalized LSM theorems in 1D using matrix product state representations and the representation theory of groups.

cond-mat.str-el↗

arXiv2018

On the classification of topological defects and textures

Ordered phases resulting from spontaneously broken continuous symmetries are effectively described by sigma models of maps to the coset space of Goldstone modes. A classic problem is to classify the topological sectors of the sigma model. In simple cases, this can be expressed in terms of homotopy groups of the target space; but in general, it is a complicated affair -- even in two dimensions -- and a general method is lacking. In this letter, we introduce a technique to systematically classify topological sectors of sigma models in various dimensions using a framework based on higher categorical generalizations of the fundamental group. As a demonstration, we recover some known results and obtain new ones. The technique and relevant mathematical structures are described only qualitatively in this letter; details can be found in our companion paper.

cond-mat.str-el↗

arXiv2018

Higher categorical groups and the classification of topological defects and textures

Sigma models effectively describe ordered phases of systems with spontaneously broken symmetries. At low energies, field configurations fall into solitonic sectors, which are homotopically distinct classes of maps. Depending on context, these solitons are known as textures or defect sectors. In this paper, we address the problem of enumerating and describing the solitonic sectors of sigma models. We approach this problem via an algebraic topological method -- combinatorial homotopy, in which one models both spacetime and the target space with algebraic objects which are higher categorical generalizations of fundamental groups, and then counts the homomorphisms between them. We give a self-contained discussion with plenty of examples and a discussion on how our work fits in with the existing literature on higher groups in physics.

math-ph↗

arXiv2018

Unwinding Short-Range Entanglement

Symmetry-Protected Topological (SPT) phases are gapped phases of quantum matter protected by global symmetries that cannot be adiabatically deformed to a trivial phase without breaking symmetry. In this work, we show that, for several SPT phases that are short range entangled (SRE), enlarging symmetries may effectively achieve the consequences of explicitly breaking symmetries. In other words, we demonstrate that non-trivial SPT phases can be unwound to trivial ones by symmetry extension- through a path where the Hilbert space is enlarged and the Hamiltonian is invariant under an extended symmetry group applying the idea of Wang, Wen and Witten in arXiv:1705.06728. We show examples of both bosonic and fermionic SPT phases in 1+1 dimensions, including Haldane's bosonic spin chain and layers of Kitaev's fermionic Majorana chains. By adding degrees of freedom into the boundary/bulk, we can lift the zero mode degeneracy, or unwind the whole system. Furthermore, based on properties of Schur cover, we sketch a general picture of unwinding applicable to any 1+1 D bosonic SPT phase protected by on-site finite symmetry. Altogether we show that SRE states can be unwound by symmetry breaking, inversion and symmetry extension.

quant-ph↗

arXiv2018

Universal quantum computing using $(\mathbb{Z}_d)^3$ symmetry-protected topologically ordered states

Measurement-based quantum computation describes a scheme where entanglement of resource states is utilized to simulate arbitrary quantum gates via local measurements. Recent works suggest that symmetry-protected topologically non-trivial, short-ranged entanged states are promising candidates for such a resource. Miller and Miyake [NPJ Quantum Information 2, 16036 (2016)] recently constructed a particular $\mathbb{Z}_2 \times \mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry-protected topological state on the Union-Jack lattice and established its quantum computational universality. However, they suggested that the same construction on the triangular lattice might not lead to a universal resource. Instead of qubits, we generalize the construction to qudits and show that the resulting $(d-1)$ qudit nontrivial $\mathbb{Z}_d \times \mathbb{Z}_d \times \mathbb{Z}_d$ symmetry-protected topological states are universal on the triangular lattice, for $d$ being a prime number greater than 2. The same construction also holds for other 3-colorable lattices, including the Union-Jack lattice.

quant-ph↗

arXiv2017

Eigenstate phases with finite on-site non-Abelian symmetry

We study the eigenstate phases of disordered spin chains with on-site finite non-Abelian symmetry. We develop a general formalism based on standard group theory to construct local spin Hamiltonians invariant under any on-site symmetry. We then specialize to the case of the simplest non-Abelian group, $S_3$, and numerically study a particular two parameter spin-1 Hamiltonian. We observe a thermal phase and a many-body localized phase with a spontaneous symmetry breaking (SSB) from $S_3$ to $\mathbb{Z}_3$ in our model Hamiltonian. We diagnose these phases using full entanglement distributions and level statistics. We also use a spin-glass diagnostic specialized to detect spontaneous breaking of the $S_3$ symmetry down to $\mathbb{Z}_3$. Our observed phases are consistent with the possibilities outlined by Potter and Vasseur [Phys. Rev. B 94, 224206 (2016)], namely thermal/ ergodic and spin-glass many-body localized (MBL) phases. We also speculate about the nature of an intermediate region between the thermal and MBL+SSB regions where full $S_3$ symmetry exists.

cond-mat.dis-nn↗

arXiv2017

Computational Power of Symmetry-Protected Topological Phases

We consider ground states of quantum spin chains with symmetry-protected topological (SPT) order as resources for measurement-based quantum computation (MBQC). We show that, for a wide range of SPT phases, the computational power of ground states is uniform throughout each phase. This computational power, defined as the Lie group of executable gates in MBQC, is determined by the same algebraic information that labels the SPT phase itself. We prove that these Lie groups always contain a full set of single-qubit gates, thereby affirming the long-standing conjecture that general SPT phases can serve as computationally useful phases of matter.

quant-ph↗

arXiv2016

Symmetry-protected topological phases with uniform computational power in one dimension

We investigate the usefulness of ground states of quantum spin chains with symmetry-protected topological order (SPTO) for measurement-based quantum computation. We show that, in spatial dimension one, if an SPTO phase supports quantum wire, then, subject to an additional symmetry condition that is satisfied in all cases so far investigated, it can also be used for quantum computation.

quant-ph↗

arXiv2016

Detection of gapped phases of a 1D spin chain with onsite and spatial symmetries

We investigate the phase diagram of a quantum spin-1 chain whose Hamiltonian is invariant under a global onsite $A_4$, translation and lattice inversion symmetries. We detect different gapped phases characterized by SPT order and symmetry breaking using matrix product state order parameters. We observe a rich variety of phases of matter characterized by a combination of symmetry breaking and symmetry fractionalization and also the interplay between the onsite and spatial symmetries. Examples of continuous phase transitions directly between topologically nontrivial SPT phases are also observed.

cond-mat.str-el↗

arXiv2015

Ground states of 1D symmetry-protected topological phases and their utility as resource states for quantum computation

The program of classifying symmetry protected topological (SPT) phases in 1D has been recently completed and has opened the doors to study closely the properties of systems belonging to these phases. It was recently found that being able to constrain the form of ground states of SPT order based on symmetry properties also allows to explore novel resource states for processing of quantum information. In this paper, we generalize the consideration of Else et al. [Phys. Rev. Lett. {\bf 108}, 240505 (2012)] where it was shown that the ground-state form of spin-1 chains protected by $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry supports perfect operation of the identity gate, important also for long-distance transmission of quantum information. We develop a formalism to constrain the ground-state form of SPT phases protected by any arbitrary finite symmetry group and use it to examine examples of ground states of SPT phases protected by various finite groups for similar gate protections. We construct a particular Hamiltonian invariant under $A_4$ symmetry transformation which is one of the groups that allows protected identity operation and examine its ground states. We find that there is an extended region where the ground state is the AKLT state, which not only supports the identity gate but also arbitrary single-qubit gates.

quant-ph↗

arXiv2012

Effect of earth rotation on pair production of Standard Model Higgs bosons at linear colliders in the noncommutative space-time

We study the neutral Higgs boson pair production through $e^{+} e^{-}$ collision in the noncommutative(NC) extension of the standard model using the Seiberg-Witten maps of this to the first order of the noncommutative parameter $Θ_{μν}$. This process is forbidden in the standard model at the tree level with background space-time being commutative. After including the effects of earth's rotation we analyse the time-averaged cross section of the pair production of Higgs boson (in the light of LEP II and LHC data) at the future Linear Collider which can be quite significant for the NC scale $Λ$ lying in the range $0.3 - 1.0$ TeV. For the 125 GeV Higgs mass(the most promising value of Higgs mass as reported by LHC), we find the NC scale as $330 \rm{GeV}$ $\le Λ\le 660 \rm{GeV}$ and using $m_h = 129(127.5) \rm{GeV}$ (the lower threshold value of the excluded region of $m_h$ reported by ATLAS(CMS) collaborations of LHC), we find the bound on $Λ$ as: (i) $339 (336) \rm{GeV} \le Λ\le 677 (670) \rm{GeV}$ corresponding to the Linear Collider energy $E_{com} = 500 \rm{GeV}$.

hep-ph↗

arXiv2012

Laboratory frame analysis of $e^+ e^- \to μ^+ μ^-$ scattering in the Noncommutative Standard Model

We study the muon pair production $ e^+ e^- \to μ^+ μ^-$ in the framework of the non-minimal noncommutative(NC) standard model to the second order of the NC parameter $Θ_{μν}$. The $\mathcal{O}(Θ^2)$ momentum dependent NC interaction significantly modifies the cross section and angular distributions which are different from the standard model. After including the effects of earth's rotation we analyse the time-averaged and time dependent observables in detail. The time-averaged azimuthal distribution of the cross section shows siginificant departure from the standard model. We find strong dependence of the total cross section(time- averaged) and their distributions on the orientation of the noncommutative electric vector (${\vecΘ}_E$). The periodic variation of the total cross-section with time over a day seems to be startling and can be thoroughly probed at the upcoming Linear Collider(LC).

hep-ph↗

arXiv2010

Tipping of a classical point mass pendulum: Role of statistical fluctuations

The behavior of a stationary inverted point mass pendulum pivoted at its lower end in a gravitational potential is studied under the influence of statistical fluctuations. It is shown using purely classical equations that the pendulum eventually tips over i.e evolves out of its initial position of unstable equilibrium, and, in a finite amount of time points down assuming a position of stable equilibrium. This `tipping time' is calculated by solving the appropriate Fokker- Planck equation in the overdamped limit. It is also shown that the asymptotic time solution for probability corresponds to the Boltzmann distribution, as expected for a system in stable equilibrium, and that the tipping time tends to infinity as the parameter corresponding to the strength of thermal fluctuations is tuned to zero, thereby defining the limit where one recovers the classical result that a stationary inverted point mass pendulum never tips over. The paper provides a unique perspective showing that phenomena like tipping that have been often attributed to quantum mechanics can be studied even in the domain of purely classical physics.

physics.class-ph↗