51 research outputs found

### Nonequilibrium quantum order at infinite temperature: spatiotemporal correlations and their generating functions

Localisation-protected quantum order extends the idea of symmetry breaking
and order in ground states to individual eigenstates at arbitrary energy.
Examples include many-body localised static and $\pi$-spin glasses in Floquet
systems. Such order is inherently dynamical and difficult to detect as the
order parameter typically varies randomly between different eigenstates,
requiring specific superpositions of eigenstates to be targeted by the initial
state. We show that two-time correlators overcome this, reflecting the presence
or absence of eigenstate order even in fully-mixed, $infinite$ $temperature$
states. We show how spatiotemporal correlators are generated by the recently
introduced dynamical potentials, demonstrating this explicitly using an Ising
and a Floquet $\pi$-spin glass and focusing on features mirroring those of
equilibrium statistical mechanics such as bimodal potentials in the
symmetry-broken phase.Comment: 9 pages, 5 figure

### Disordered Chern insulator with a two step Floquet drive

We explore the physics of a Chern insulator subjected to a two step Floquet
drive. We analytically obtain the phase diagram and show that the system can
exhibit different topological phases characterized by presence and chirality of
edge-modes in the two bulk gaps of the Floquet quasienergy spectrum, around $0$
and $\pi$. We find that the phase of the system depends on the mean but not on
the amplitude of the drive. The bulk topological invariants characterizing the
phases can be extracted by mapping the unitary evolution within a time period
to an energetically trivial but topologically non-trivial time evolution. An
extensive numerical study of the bulk topological invariants in the presence of
quenched disorder reveals new transitions induced by strong disorder (i) from
the different topological to trivial insulator phases and (ii) from a trivial
to a topological Anderson insulator phase at intermediate disorder strengths.
Careful analysis of level statistics of the quasienergy spectrum indicates a
`levitation-annihilation' mechanism near these transitions.Comment: 15 pages, 10 figures, version published in Phys. Rev.

### Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions

Many-body localisation is studied in a disordered quantum spin-1/2 chain with
long-ranged power-law interactions, and distinct power-law exponents for
interactions between longitudinal and transverse spin components. Using a
self-consistent mean-field theory centring on the local propagator in Fock
space and its associated self-energy, a localisation phase diagram is obtained
as a function of the power-law exponents and the disorder strength of the
random fields acting on longitudinal spin-components. Analytical results are
corroborated using the well-studied and complementary numerical diagnostics of
level statistics, entanglement entropy, and participation entropy, obtained via
exact diagonalisation. We find that increasing the range of interactions
between transverse spin components hinders localisation and enhances the
critical disorder strength. In marked contrast, increasing the interaction
range between longitudinal spin components is found to enhance localisation and
lower the critical disorder.Comment: 30 pages, 4 figure

### Probing surface states exposed by crystal terminations at arbitrary orientations of three-dimensional topological insulators

The topological properties of the bulk band structure of a three-dimensional
topological insulator (TI) manifest themselves in the form of metallic surface
states. In this paper, we propose a probe which directly couples to an exotic
property of these surface states, namely the spin-momentum locking. We show
that the information regarding the spin textures, so extracted, for different
surfaces can be put together to reconstruct the parameters characterizing the
bulk band structure of the material, hence acting as a hologram. For specific
TI materials like, $\text{Bi}_2\text{Se}_3, \text{Bi}_2\text{Te}_3 \text{and
Sb}_2\text{Te}_3$, the planar surface states are distinct from one another with
regard to their spectrum and the associated spin texture for each angle
($\theta$), which the normal to the surface makes with the crystal growth axis.
We develop a tunnel Hamiltonian between such arbitrary surfaces and a spin
polarized STM which provides a unique fingerprint of the dispersion and the
associated spin texture corresponding to each $\theta$. Additionally, the
theory presented in this article can be used to extract value of $\theta$ for a
given arbitrary planar surface from the STM spectra itself hence effectively
mimicking X-ray spectroscopy.Comment: 11 pages, 8 figures, version accepted in Phys. Rev.

### Locating topological phase transitions using nonequilibrium signatures in local bulk observables

Topological quantum phases cannot be characterized by local order parameters
in the bulk. In this work however, we show that signatures of a topological
quantum critical point do remain in local observables in the bulk, and manifest
themselves as non-analyticities in their expectation values taken over a family
of non-equilibrium states generated using a quantum quench protocol. The
signature can be used for precisely locating the critical points in parameter
space. A large class of initial states can be chosen for the quench (including
finite temperature states), the sufficient condition being existence of a
finite occupation-gradient with respect to energy for the single-particle
critical mode. We demonstrate these results in tractable models of
non-interacting fermions exhibiting topological phase transitions in one and
two spatial dimensions. We also show that the non-analyticities can be absent
if the gap-closing is non-topological, i.e., when it corresponds to no phase
transition.Comment: 4.5 pages, 5 figures + supplementary material, version published in
Phys. Rev. B as a Rapid Communicatio

### Anatomy of localisation protected quantum order on Hilbert space

Many-body localised phases of disordered, interacting quantum systems allow
for exotic localisation protected quantum order in eigenstates at arbitrarily
high energy densities. In this work, we analyse the manifestation of such order
on the Hilbert-space anatomy of eigenstates. Quantified in terms of non-local
Hilbert-spatial correlations of eigenstate amplitudes, we find that the spread
of the eigenstates on the Hilbert-space graph is directly related to the order
parameters which characterise the localisation protected order, and hence these
correlations, in turn, characterise the order or lack thereof. Higher-point
eigenstate correlations also characterise the different entanglement structures
in the many-body localised phases, with and without order, as well as in the
ergodic phase. The results pave the way for characterising the transitions
between many-body localised phases and the ergodic phase in terms of scaling of
emergent correlation lengthscales on the Hilbert-space graph.Comment: 28 pages, 7 figures, Invited article for J. Phys.: Condens. Matter
special issue -- Emerging Leaders 202

### Fidelity, Rosen-Zener Dynamics, Entropy and Decoherence in one dimensional hard-core bosonic systems

We study the non-equilibrium dynamics of a one-dimensional system of hard
core bosons (HCBs) in the presence of an onsite potential (with an alternating
sign between the odd and even sites) which shows a quantum phase transition
(QPT) from the superfluid (SF) phase to the so-called "Mott Insulator" (MI)
phase. The ground state quantum fidelity shows a sharp dip at the quantum
critical point (QCP) while the fidelity susceptibility shows a divergence right
there with its scaling given in terms of the correlation length exponent of the
QPT. We then study the evolution of this bosonic system following a quench in
which the magnitude of the alternating potential is changed starting from zero
(the SF phase) to a non-zero value (the MI phase) according to a half Rosen
Zener (HRZ) scheme or brought back to the initial value following a full Rosen
Zener (FRZ) scheme. The local von Neumann entropy density is calculated in the
final MI phase (following the HRZ quench) and is found to be less than the
equilibrium value ($\log 2$) due to the defects generated in the final state as
a result of the quenching starting from the QCP of the system. We also briefly
dwell on the FRZ quenching scheme in which the system is finally in the SF
phase through the intermediate MI phase and calculate the reduction in the
supercurrent and the non-zero value of the residual local entropy density in
the final state. Finally, the loss of coherence of a qubit (globally and weekly
coupled to the HCB system) which is initially in a pure state is investigated
by calculating the time-dependence of the decoherence factor when the HCB chain
evolves under a HRZ scheme starting from the SF phase. This result is compared
with that of the sudden quench limit of the half Rosen-Zener scheme where an
exact analytical form of the decoherence factor can be derived.Comment: To appear in European Physical Journal

### Tunnel Magnetoresistance scan of a pristine three-dimensional topological insulator

Though the Fermi surface of surface states of a 3D topological insulator (TI)
has zero magnetization, an arbitrary segment of the full Fermi surface has a
unique magnetic moment consistent with the type of spin-momentum locking in
hand. We propose a three-terminal set up, which directly couples to the
magnetization of a chosen segment of a Fermi surface hence leading to a finite
tunnel magnetoresistance (TMR) response of the nonmagnetic TI surface states,
when coupled to spin polarized STM probe. This multiterminal TMR not only
provides a unique signature of spin-momentum locking for a pristine TI but also
provides a direct measure of momentum resolved out of plane polarization of
hexagonally warped Fermi surfaces relevant for $Bi_2Te_3$, which could be as
comprehensive as spin-resolved ARPES. Implication of this unconventional TMR is
also discussed in the broader context of 2D spin-orbit (SO) materials.Comment: Version accepted in Phys. Rev. B (Rapid Communications

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