Explanipedia

Scaling of entanglement entropy at quantum critical points in random spin chains Open

Prashant Kumar, R. N. Bhatt · 2023

We study the scaling properties of the entanglement entropy (EE) near quantum critical points in interacting random antiferromagnetic (AF) spin chains. Using density-matrix renormalization group, we compute the half-chain EE near the topol…

Entanglement Entropy Growth in Disordered Spin Chains with Tunable Range Interactions Open

Youcef Mohdeb, Javad Vahedi, R. N. Bhatt, Stephan Haas, Stefan Kettemann · 2023

The non-equilibrium dynamics of disordered many-body quantum systems after a global quantum quench unveils important insights about the competition between interactions and disorder, yielding in particular an insightful perspective on many…

Possible continuous transition from fractional quantum Hall to stripe phase at Open

Prashant Kumar, R. N. Bhatt · 2022

We study the phase diagram of $\\nu_e=7/3$ state in the $N=1$ Landau level in\nthe presence of band mass anisotropy. Using density matrix renormalization\ngroup on an infinite cylinder geometry, we find a continuous transition from\nthe to…

Geometry, Disorder and Phase Transitions in Topological States of Matter Open

R. N. Bhatt, Frederick Haldane, E. H. Rezayi, Kun Yang · 2022

The quantum Hall effect is the birthplace of topological states of matter, a major theme at the forefront of condensed matter physics in the past two decades. The fractional quantum Hall (FQH) effect revolutionized our understanding of pha…

Phil was different: A personal appreciation Open

R. N. Bhatt · 2021

Anisotropic quantum Hall states in the presence of interactions with fourfold rotational symmetry Open

Prashant Kumar, R. N. Bhatt · 2021

We study the effects of anisotropic interactions in the quantum Hall effect in the presence of a fourfold discrete rotational (C₄) symmetry. Employing the density matrix renormalization group technique on an infinite cylinder ge…

Beyond the universal Dyson singularity for 1-D chains with hopping disorder Open

Akshay Krishna, R. N. Bhatt · 2021

Topology and many-body localization Open

R. N. Bhatt, Akshay Krishna · 2021

Entanglement properties of disordered quantum spin chains with long-range antiferromagnetic interactions Open

Y. Mohdeb, Javad Vahedi, N. Moure, A. Roshani, Hyun‐Yong Lee , et al. · 2020

Entanglement measures are useful tools in characterizing otherwise unknown quantum phases and indicating transitions between them. Here we examine the concurrence and entanglement entropy in quantum spin chains with random long-range coupl…

Floquet dynamics of disordered bands with isolated critical energies Open

Sriram Ganeshan, Kartiek Agarwal, R. N. Bhatt · 2020

We investigate localization properties of driven models which exhibit a subextensive number of extended states in the static setting. We consider instances where the extended modes are or are not protected by topological considerations. To…

Beyond universal behavior in the one-dimensional chain with random nearest-neighbor hopping Open

Akshay Krishna, R. N. Bhatt · 2020

Here, we study the one-dimensional nearest-neighbor tight-binding model of electrons with independently distributed random hopping and no on-site potential (i.e., off-diagonal disorder with particle-hole symmetry, leading to sublattice sym…

Localization and interactions in topological and nontopological bands in two dimensions Open

Akshay Krishna, Matteo Ippoliti, R. N. Bhatt · 2019

A two-dimensional electron gas in a high magnetic field displays macroscopically degenerate Landau levels, which can be split into Hofstadter subbands by means of a weak periodic potential. By carefully engineering such a potential, one ca…

Interaction-dependent anisotropy of fractional quantum Hall states Open

Akshay Krishna, Fan Chen, Matteo Ippoliti, R. N. Bhatt · 2019

In the absence of rotational symmetry, a fractional quantum Hall (FQH) system can exploit a geometric degree of freedom to minimize its ground-state energy. The mass anisotropy of bare particles interacting isotropically is partially inher…

Cooling arbitrary near-critical systems using hyperbolic quenches Open

Prahar Mitra, Matteo Ippoliti, R. N. Bhatt, S. L. Sondhi, Kartiek Agarwal · 2019

We describe a quench protocol that allows the rapid preparation of ground states of arbitrary interacting conformal field theories in 1+1 dimensions. We start from the ground state of a related gapped relativistic quantum field theory and …

Localization-length exponent in two models of quantum Hall plateau transitions Open

Qiong Zhu, Peng Wu, R. N. Bhatt, Xin Wan · 2019

Motivated by the recent numerical studies on the Chalker-Coddington network model that found a larger-than-expected critical exponent of the localization length characterizing the integer quantum Hall plateau transitions, we revisited the …

Many-body localization in Landau-level subbands Open

Akshay Krishna, Matteo Ippoliti, R. N. Bhatt · 2019

We explore the problem of localization in topological and non-topological\nnearly-flat subbands derived from the lowest Landau level, in the presence of\nquenched disorder and short-range interactions. We consider two models: a\nsuitably e…

Geometry of flux attachment in anisotropic fractional quantum Hall states Open

Matteo Ippoliti, R. N. Bhatt, F. D. M. Haldane · 2018

Fractional quantum Hall (FQH) states are known to possess an internal metric degree of freedom that allows them to minimize their energy when contrasting geometries are present in the problem (e.g., electron band mass and dielectric tensor…

Fast Preparation of Critical Ground States Using Superluminal Fronts Open

Kartiek Agarwal, R. N. Bhatt, S. L. Sondhi · 2018

We propose a spatiotemporal quench protocol that allows for the fast preparation of ground states of gapless models with Lorentz invariance. Assuming the system initially resides in the ground state of a corresponding massive model, we sho…

Disordered quantum spin chains with long-range antiferromagnetic interactions Open

N. Moure, Hyun‐Yong Lee, Stephan Haas, R. N. Bhatt, Stefan Kettemann · 2018

We investigate the magnetic susceptibility $\chi(T)$ of quantum spin chains of $N=1280$ spins with power-law long-range antiferromagnetic coupling as a function of their spatial decay exponent $\alpha$ and cutoff length $\xi$. The calculat…

Integer quantum Hall transition in a fraction of a Landau level Open

Matteo Ippoliti, Scott Geraedts, R. N. Bhatt · 2018

We investigate the quantum Hall problem in the lowest Landau level in two\ndimensions, in the presence of an arbitrary number of $\\delta$-function\npotentials arranged in different geometric configurations. When the number of\ndelta funct…

Heitler-London model for acceptor-acceptor interactions in doped semiconductors Open

Adam C. Durst, Kyle Castoria, R. N. Bhatt · 2017

The interactions between acceptors in semiconductors are often treated in\nqualitatively the same manner as those between donors. Acceptor wave functions\nare taken to be approximately hydrogenic and the standard hydrogen molecule\nHeitler…

Composite fermions in bands with -fold rotational symmetry Open

Matteo Ippoliti, Scott Geraedts, R. N. Bhatt · 2017

We study the effect of band anisotropy with discrete rotational symmetry\n$C_N$ (where $N\\ge 2$) in the quantum Hall regime of two-dimensional electron\nsystems. We focus on the composite Fermi liquid (CFL) at half filling of the\nlowest …

Evolution of quantum entanglement with disorder in fractional quantum Hall liquids Open

Zhao Liu, R. N. Bhatt · 2017

We present a detailed study of the ground-state entanglement in disordered\nfractional quantum Hall liquids. We consider electrons at various filling\nfractions $f$ in the lowest Landau level, with Coulomb interactions. At\n$f=1/3,1/5$ and…

Connection between Fermi contours of zero-field electrons and composite fermions in two-dimensional systems Open

Matteo Ippoliti, Scott Geraedts, R. N. Bhatt · 2017

We investigate the relation between the Fermi sea (FS) of zero-field carriers\nin two-dimensional systems and the FS of the corresponding composite fermions\nwhich emerge in a high magnetic field at filling $\\nu = \\frac{1}{2}$, as the\nk…

Localization and transport in a strongly driven Anderson insulator Open

Kartiek Agarwal, Sriram Ganeshan, R. N. Bhatt · 2017

We study localization and charge dynamics in a monochromatically driven\none-dimensional Anderson insulator focussing on the low-frequency,\nstrong-driving regime. We study this problem using a mapping of the Floquet\nHamiltonian to a hopp…

Numerical study of anisotropy in a composite Fermi liquid Open

Matteo Ippoliti, Scott Geraedts, R. N. Bhatt · 2017

We perform density-matrix renormalization group studies of a two-dimensional\nelectron gas in a high magnetic field and with an anisotropic band mass. At\nhalf-filling in the lowest Landau level, such a system is a Fermi liquid of\ncomposi…

Emergent local integrals of motion without a complete set of localized eigenstates Open

Scott Geraedts, R. N. Bhatt, Rahul Nandkishore · 2017

Systems where all energy eigenstates are localized are known to display an\nemergent local integrability, in the sense that one can construct an extensive\nnumber of operators that commute with the Hamiltonian and are localized in real\nsp…

Surface code architecture for donors and dots in silicon with imprecise and nonuniform qubit couplings Open

Giuseppe Pica, Brendon W. Lovett, R. N. Bhatt, T. Schenkel, S. A. Lyon · 2016

A scaled quantum computer with donor spins in silicon would benefit from a viable semiconductor framework and a strong inherent decoupling of the qubits from the noisy environment. Coupling neighboring spins via the natural exchange intera…

Probing the geometry of the Laughlin state Open

Sonika Johri, Zlatko Papić, Peter Schmitteckert, R. N. Bhatt, F. D. M. Haldane · 2016

It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive num…

Many-Body Localization in Imperfectly Isolated Quantum Systems Open

Sonika Johri, Rahul Nandkishore, R. N. Bhatt · 2015

We use numerical exact diagonalization to analyze which aspects of the many-body localization phenomenon survive in an imperfectly isolated setting, when the system of interest is weakly coupled to a thermalizing environment. We show that …

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