arXiv subjects

Diptiman Sen

Publications and source records attributed to Diptiman Sen.

At least 109 records · Page 6Linked to original sources

arXiv2011

Quenching across quantum critical points in periodic systems: dependence of scaling laws on periodicity

We study the quenching dynamics of a many-body system in one dimension described by a Hamiltonian that has spatial periodicity. Specifically, we consider a spin-1/2 chain with equal xx and yy couplings and subject to a periodically varying magnetic field in the z direction or, equivalently, a tight-binding model of spinless fermions with a periodic local chemical potential, having period 2q, where q is a natural number. For a linear quench of the magnetic field strength (or potential strength) at rate 1/τacross a quantum critical point, we find that the density of defects thereby produced scales as 1/τ^{q/(q+1)}, deviating from the 1/\sqrtτ scaling that is ubiquitous to a range of systems. We analyze this behavior by mapping the low-energy physics of the system to a set of fermionic two-level systems labeled by the lattice momentum k undergoing a non-linear quench as well as by performing numerical simulations. We also find that if the magnetic field is a superposition of different periods, the power law depends only on the smallest period for very large values of τalthough it may exhibit a cross-over at intermediate values of τ. Finally, for the case where a zz coupling is also present in the spin chain, or equivalently, where interactions are present in the fermionic system, we argue that the power associated with the scaling law depends on a combination of q and interaction strength.

cond-mat.str-el↗

arXiv2011

Microscopic study of the 2/5 fractional quantum Hall edge

This paper reports on our study of the edge of the 2/5 fractional quantum Hall state, which is more complicated than the edge of the 1/3 state because of the presence of a continuum of quasi-degenerate edge sectors corresponding to different partitions of composite fermions in the lowest two Λ levels. The addition of an electron at the edge is a non-perturbative process and it is not a priori obvious in what manner the added electron distributes itself over these sectors. We show, from a microscopic calculation, that when an electron is added at the edge of the ground state in the [N_1, N_2] sector, where N_1 and N_2 are the numbers of composite fermions in the lowest two Λ levels, the resulting state lies in either [N_1 + 1, N_2] or [N_1, N_2 + 1] sector; adding an electron at the edge is thus equivalent to adding a composite fermion at the edge. The coupling to other sectors of the form [N_1 + 1 + k, N_2 - k], k integer, is negligible in the asymptotically low-energy limit. This study also allows a detailed and substantial comparison with the two-boson model of the 2/5 edge. We compute the spectral weights and find that while the individual spectral weights are complicated and non-universal, their sum is consistent with an effective two-boson description of the 2/5 edge.

cond-mat.str-el↗

arXiv2011

Exact Entanglement Studies of Strongly Correlated Systems: Role of Long-Range Interactions and Symmetries of the System

We study the bipartite entanglement of strongly correlated systems using exact diagonalization techniques. In particular, we examine how the entanglement changes in the presence of long-range interactions by studying the Pariser-Parr-Pople model with long-range interactions. We compare the results for this model with those obtained for the Hubbard and Heisenberg models with short-range interactions. This study helps us to understand why the density matrix renormalization group (DMRG) technique is so successful even in the presence of long-range interactions. To better understand the behavior of long-range interactions and why the DMRG works well with it, we study the entanglement spectrum of the ground state and a few excited states of finite chains. We also investigate if the symmetry properties of a state vector have any significance in relation to its entanglement. Finally, we make an interesting observation on the entanglement profiles of different states (across the energy spectrum) in comparison with the the corresponding profile of the density of states. We use isotropic chains and a molecule with non-Abelian symmetry for these numerical investigations.

quant-ph↗

arXiv2011

Conductance of Tomonaga-Luttinger liquid wires and junctions with resistances

We study the effect that resistive regions have on the conductance of a quantum wire with interacting electrons which is connected to Fermi liquid leads. Using the bosonization formalism and a Rayleigh dissipation function to model the power dissipation, we use both scattering theory and Green's function techniques to derive the DC conductance. The resistive regions are generally found to lead to incoherent transport. For a single wire, we find that the resistance adds in series to the contact resistance of h/e^2 for spinless electrons, and the total resistance is independent of the Luttinger parameter K_W of the wire. We numerically solve the bosonic equations to illustrate what happens when a charge density pulse is incident on the wire; the results depend on the parameters of the resistive and interacting regions in interesting ways. For a junction of Tomonaga-Luttinger liquid wires, we use a dissipationless current splitting matrix to model the junction. For a junction of three wires connected to Fermi liquid leads, there are two families of such matrices; we find that the conductance matrix generally depends on K_W for one family but is independent of K_W for the other family, regardless of the resistances present in the system.

cond-mat.mes-hall↗

arXiv2011

Model of resistances in systems of Tomonaga-Luttinger liquid wires

In a recent paper, we combined the technique of bosonization with the concept of a Rayleigh dissipation function to develop a model for resistances in one-dimensional systems of interacting spinless electrons [arXiv:1011.5058]. We also studied the conductance of a system of three wires by using a current splitting matrix M at the junction. In this paper we extend our earlier work in several ways. The power dissipated in a three-wire system is calculated as a function of M and the voltages applied in the leads. By combining two junctions of three wires, we examine a system consisting of two parallel resistances. We study the conductance of this system as a function of the M matrices and the two resistances; we find that the total resistance is generally quite different from what one expects for a classical system of parallel resistances. We will do a sum over paths to compute the conductance of this system when one of the two resistances is taken to be infinitely large. Finally we study the conductance of a three-wire system of interacting spin-1/2 electrons, and show that the charge and spin conductances can generally be different from each other.

cond-mat.mes-hall↗

arXiv2011

Topological phases, Majorana modes and quench dynamics in a spin ladder system

We explore the salient features of the `Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections between spin phases and topologically non-trivial phases of non-interacting fermionic systems, demonstrating the equivalence between the spontaneous breaking of global Z2 symmetry in spin systems and the existence of isolated Majorana modes. In the Kitaev ladder, we investigate topological properties of the system in different sectors characterized by the presence or absence of a vortex in each plaquette of the ladder. We show that vortex patterns can yield a rich parameter space for tuning into topologically non-trivial phases. We introduce a new topological invariant which explicitly determines the presence of zero energy Majorana modes at the boundaries of such phases. Finally, we discuss dynamic quenching between topologically non-trivial phases in the Kitaev ladder, and in particular, the post-quench dynamics governed by tuning through a quantum critical point.

cond-mat.str-el↗

arXiv2010

Spin-1 Kitaev model in one dimension

We study a one-dimensional version of the Kitaev model on a ring of size N, in which there is a spin S > 1/2 on each site and the Hamiltonian is J \sum_i S^x_i S^y_{i+1}. The cases where S is integer and half-odd-integer are qualitatively different. We show that there is a Z_2 valued conserved quantity W_n for each bond (n,n+1) of the system. For integer S, the Hilbert space can be decomposed into 2^N sectors, of unequal sizes. The number of states in most of the sectors grows as d^N, where d depends on the sector. The largest sector contains the ground state, and for this sector, for S=1, d =(\sqrt{5}+1)/2. We carry out exact diagonalization for small systems. The extrapolation of our results to large N indicates that the energy gap remains finite in this limit. In the ground state sector, the system can be mapped to a spin-1/2 model. We develop variational wave functions to study the lowest energy states in the ground state and other sectors. The first excited state of the system is the lowest energy state of a different sector and we estimate its excitation energy. We consider a more general Hamiltonian, adding a term λ\sum_n W_n, and show that this has gapless excitations in the range λ^c_1 \leq λ\leq λ^c_2. We use the variational wave functions to study how the ground state energy and the defect density vary near the two critical points λ^c_1 and λ^c_2.

cond-mat.stat-mech↗

arXiv2010

Quenching across quantum critical points: role of topological patterns

We introduce a one-dimensional version of the Kitaev model consisting of spins on a two-legged ladder and characterized by Z_2 invariants on the plaquettes of the ladder. We map the model to a fermionic system and identify the topological sectors associated with different Z_2 patterns in terms of fermion occupation numbers. Within these different sectors, we investigate the effect of a linear quench across a quantum critical point. We study the dominant behavior of the system by employing a Landau-Zener-type analysis of the effective Hamiltonian in the low-energy subspace for which the effective quenching can sometimes be non-linear. We show that the quenching leads to a residual energy which scales as a power of the quenching rate, and that the power depends on the topological sectors and their symmetry properties in a non-trivial way. This behavior is consistent with the general theory of quantum quenching, but with the correlation length exponent νbeing different in different sectors.

cond-mat.stat-mech↗

arXiv2010

Nonadiabatic charge pumping by oscillating potentials in one dimension: results for infinite system and finite ring

We study charge pumping when a combination of static potentials and potentials oscillating with a time period T is applied in a one-dimensional system of non-interacting electrons. We consider both an infinite system using the Dirac equation in the continuum approximation, and a periodic ring with a finite number of sites using the tight-binding model. The infinite system is taken to be coupled to reservoirs on the two sides which are at the same chemical potential and temperature. We consider a model in which oscillating potentials help the electrons to access a transmission resonance produced by the static potentials, and show that non-adiabatic pumping violates the simple \sin ϕrule which is obeyed by adiabatic two-site pumping. For the ring, we do not introduce any reservoirs, and we present a method for calculating the current averaged over an infinite time using the time evolution operator U(T) assuming a purely Hamiltonian evolution. We analytically show that the averaged current is zero if the Hamiltonian is real and time reversal invariant. Numerical studies indicate another interesting result, namely, that the integrated current is zero for any time-dependence of the potential if it is applied to only one site. Finally we study the effects of pumping at two sites on a ring at resonant and non-resonant frequencies, and show that the pumped current has different dependences on the pumping amplitude in the two cases.

cond-mat.mes-hall↗

arXiv2010

Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton

According to Wen's theory, a universal behavior of the fractional quantum Hall edge is expected at sufficiently low energies, where the dispersion of the elementary edge excitation is linear. A microscopic calculation shows that the actual dispersion is indeed linear at low energies, but deviates from linearity beyond certain energy, and also exhibits an "edge roton minimum." We determine the edge exponent from a microscopic approach, and find that the nonlinearity of the dispersion makes a surprisingly small correction to the edge exponent even at energies higher than the roton energy. We explain this insensitivity as arising from the fact that the energy at maximum spectral weight continues to show an almost linear behavior up to fairly high energies. We also formulate an effective field theory to describe the behavior of a reconstructed edge, taking into account multiple edge modes. Experimental consequences are discussed.

cond-mat.str-el↗

arXiv2010

Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

We discuss a technique for solving the Landau-Zener (LZ) problem of finding the probability of excitation in a two-level system. The idea of time reversal for the Schrodinger equation is employed to obtain the state reached at the final time and hence the excitation probability. Using this method, which can reproduce the well-known expression for the LZ transition probability, we solve a variant of the LZ problem which involves waiting at the minimum gap for a time t_w; we find an exact expression for the excitation probability as a function of t_w. We provide numerical results to support our analytical expressions. We then discuss the problem of waiting at the quantum critical point of a many-body system and calculate the residual energy generated by the time-dependent Hamiltonian. Finally we discuss possible experimental realizations of this work.

cond-mat.stat-mech↗

arXiv2010

Modified DMRG algorithm for the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange: Comparison with field theory at large $J_2/J_1$

A modified density matrix renormalization group (DMRG) algorithm is applied to the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange $J_1$, $J_2$ between first and second neighbors. The modified algorithm yields accurate results up to $J_2/J_1 \approx 4$ for the magnetic gap $Δ$ to the lowest triplet state, the amplitude $B$ of the bond order wave (BOW) phase, the wavelength $λ$ of the spiral phase, and the spin correlation length $ξ$. The $J_2/J_1$ dependences of $Δ$, $B$, $λ$ and $ξ$ provide multiple comparisons to field theories of the zigzag chain. The twist angle of the spiral phase and the spin structure factor yield additional comparisons between DMRG and field theory. Attention is given to the numerical accuracy required to obtain exponentially small gaps or exponentially long correlations near a quantum phase transition.

cond-mat.str-el↗

arXiv2010

Power dissipation for systems with junctions of multiple quantum wires

We study power dissipation for systems of multiple quantum wires meeting at a junction, in terms of a current splitting matrix (M) describing the junction. We present a unified framework for studying dissipation for wires with either interacting electrons (i.e., Tomonaga-Luttinger liquid wires with Fermi liquid leads) or non-interacting electrons. We show that for a given matrix M, the eigenvalues of M^T M characterize the dissipation, and the eigenvectors identify the combinations of bias voltages which need to be applied to the different wires in order to maximize the dissipation associated with the junction. We use our analysis to propose and study some microscopic models of a dissipative junction which employ the edge states of a quantum Hall liquid. These models realize some specific forms of the M-matrix whose entries depends on the tunneling amplitudes between the different edges.

cond-mat.mes-hall↗

arXiv2009

Entanglement production due to quench dynamics of an anisotropic XY chain in a transverse field

We compute concurrence and negativity as measures of two-site entanglement generated by a power-law quench (characterized by a rate 1/tau and an exponent alpha) which takes an anisotropic XY chain in a transverse field through a quantum critical point (QCP). We show that only the even-neighbor pairs of sites get entangled in such a process. Moreover, there is a critical rate of quench, 1/tau_c, above which no two-site entanglement is generated; the entire entanglement is multipartite. The ratio of the two-site entanglements between consecutive even neighbors can be tuned by changing the quench rate. We also show that for large tau, the concurrence (negativity) scales as sqrt{alpha/tau} (alpha/tau), and we relate this scaling behavior to defect production by the quench through a QCP.

cond-mat.stat-mech↗

arXiv2009

Defect production due to quenching through a multicritical point and along a gapless line

In this review, we study the quenching dynamics of a one-dimensional XY Hamiltonian in a transverse field under linear variation of different parameters of the Hamiltonian so that the system is driven through various critical points and gapless lines. It is observed that the density of defects falls off as a power law with the quenching rate $1/τ$ where the power law is determined by the dimensionality of the underlying lattice and the critical exponents associated with the quantum critical point as predicted by Kibble-Zurek scaling. However, we show that when the system is driven through a multicritical point or along a gapless line, Kibble Zurek scaling needs to be modified. We discuss generalized scaling forms of the defect density for the above two situations.

cond-mat.stat-mech↗

arXiv2009

The virial expansion of a classical interacting system

We consider N particles interacting pair-wise by an inverse square potential in one dimension (Calogero-Sutherland-Moser model). When trapped harmonically, its classical canonical partition function for the repulsive regime is known in the literature. We start by presenting a concise re-derivation of this result. The equation of state is then calculated both for the trapped and the homogeneous gas. Finally, the classical limit of Wu's distribution function for fractional exclusion statistics is obtained and we re-derive the classical virial expansion of the homogeneous gas using this distribution function.

cond-mat.stat-mech↗

arXiv2009

Non-equilibrium dynamics of quantum systems: order parameter evolution, defect generation, and qubit transfer

In this review, we study some aspects of the non-equilibrium dynamics of quantum systems. In particular, we consider the effect of varying a parameter in the Hamiltonian of a quantum system which takes it across a quantum critical point or line. We study both sudden and slow quenches in a variety of systems including one-dimensional ultracold atoms in an optical lattice, an infinite range ferromagnetic Ising model, and some exactly solvable spin models in one and two dimensions (such as the Kitaev model). We show that quenching leads to the formation of defects whose density has a power-law dependence on the quenching rate; the power depends on the dimensionalities of the system and of the critical surface and on some of the exponents associated with the critical point which is being crossed. We also study the effect of non-linear quenching; the power law of the defects then depends on the degree of non-linearity. Finally, we study some spin-1/2 models to discuss how a qubit can be transferred across a system.

cond-mat.stat-mech↗

arXiv2009

AC conductivity of a quantum Hall line junction

We present a microscopic model for calculating the AC conductivity of a finite length line junction made up of two counter or co-propagating single mode quantum Hall edges with possibly different filling fractions. The effect of density-density interactions and the tunneling conductance (σ), between the two edges, is considered, and exact expressions are derived for the AC conductivity as a function of the frequency (ω), the length of the line junction and other parameters of the system. We reproduce the results of Phys. Rev. B 78, 085430 (2008) in the DC limit (ω\to 0), and generalize those results for an interacting system. As a function of ω, the AC conductivity shows significant oscillations if σis small; the oscillations become less prominent as σincreases. A renormalization group analysis shows that the system may be in a metallic or an insulating phase depending on the strength of the interactions. We discuss the experimental implications of this for the behavior of the AC conductivity at low temperatures.

cond-mat.mes-hall↗