arXiv subjects

Diptiman Sen

Publications and source records attributed to Diptiman Sen.

At least 127 records · Page 7Linked to original sources

arXiv2009

Nonequilibrium charge transport in an interacting open system: two-particle resonance and current asymmetry

We use Lippman-Schwinger scattering theory to study nonequilibrium electron transport through an interacting open quantum dot. The two-particle current is evaluated exactly while we use perturbation theory to calculate the current when the leads are Fermi liquids at different chemical potentials. We find an interesting two-particle resonance induced by the interaction and obtain criteria to observe it when a small bias is applied across the dot. Finally, for a system without spatial inversion symmetry we find that the two-particle current is quite different depending on whether the electrons are incident from the left lead or the right lead.

cond-mat.mes-hall↗

arXiv2009

Enhancement of tunneling density of states at a junction of three Luttinger liquid wires

We study the tunneling density of states (TDOS) for a junction of three Tomonaga-Luttinger liquid wires. We show that there are fixed points which allow for the enhancement of the TDOS, which is unusual for Luttinger liquids. The distance from the junction over which this enhancement occurs is of the order of x = v/(2 ω), where v is the plasmon velocity and ωis the bias frequency. Beyond this distance, the TDOS crosses over to the standard bulk value independent of the fixed point describing the junction. This finite range of distances opens up the possibility of experimentally probing the enhancement in each wire individually.

cond-mat.mes-hall↗

arXiv2009

Effect of inter-edge Coulomb interactions on transport through a point contact in a ν= 5/2 quantum Hall state

We study transport across a point contact separating two line junctions in a ν= 5/2 quantum Hall system. We analyze the effect of inter-edge Coulomb interactions between the chiral bosonic edge modes of the half-filled Landau level (assuming a Pfaffian wave function for the half-filled state) and of the two fully filled Landau levels. In the presence of inter-edge Coulomb interactions between all the six edges participating in the line junction, the stable fixed point corresponds to a point contact which is neither fully opaque nor fully transparent. Remarkably, this fixed point represents a situation where the half-filled level is fully transmitting, while the two filled levels are completely backscattered; hence the fixed point Hall conductance is given by G_H = {1/2} e^2/h. We predict the non-universal temperature power laws by which the system approaches the stable fixed point from the two unstable fixed points corresponding to the fully connected case (G_H = {5/2} e^2/h) and the fully disconnected case (G_H = 0).

cond-mat.mes-hall↗

arXiv2009

Defect production due to quenching through a multicritical point

We study the generation of defects when a quantum spin system is quenched through a multicritical point by changing a parameter of the Hamiltonian as $t/τ$, where $τ$ is the characteristic time scale of quenching. We argue that when a quantum system is quenched across a multicritical point, the density of defects ($n$) in the final state is not necessarily given by the Kibble-Zurek scaling form $n \sim 1/τ^{d ν/(z ν+1)}$, where $d$ is the spatial dimension, and $ν$ and $z$ are respectively the correlation length and dynamical exponent associated with the quantum critical point. We propose a generalized scaling form of the defect density given by $n \sim 1/τ^{d/(2z_2)}$, where the exponent $z_2$ determines the behavior of the off-diagonal term of the $2 \times 2$ Landau-Zener matrix at the multicritical point. This scaling is valid not only at a multicritical point but also at an ordinary critical point.

cond-mat.stat-mech↗

arXiv2008

Quenching along a gapless line: A different exponent for defect density

We use a new quenching scheme to study the dynamics of a one-dimensional anisotropic $XY$ spin-1/2 chain in the presence of a transverse field which alternates between the values $h+\de$ and $h-\de$ from site to site. In this quenching scheme, the parameter denoting the anisotropy of interaction ($\ga$) is linearly quenched from $-\infty$ to $ +\infty$ as $\ga = t/τ$, keeping the total strength of interaction $J$ fixed. The system traverses through a gapless phase when $\ga$ is quenched along the critical surface $h^2 = \de^2 + J^2$ in the parameter space spanned by $h$, $\de$ and $\ga$. By mapping to an equivalent two-level Landau-Zener problem, we show that the defect density in the final state scales as $1/τ^{1/3}$, a behavior that has not been observed in previous studies of quenching through a gapless phase. We also generalize the model incorporating additional alternations in the anisotropy or in the strength of the interaction, and derive an identical result under a similar quenching. Based on the above results, we propose a general scaling of the defect density with the quenching rate $τ$ for quenching along a gapless critical line.

cond-mat.stat-mech↗

arXiv2008

Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions

In the first part of this paper, we study the spin-S Kitaev model using spin wave theory. We discover a remarkable geometry of the minimum energy surface in the N-spin space. The classical ground states, called Cartesian or CN-ground states, whose number grows exponentially with the number of spins N, form a set of points in the N-spin space. These points are connected by a network of flat valleys in the N-spin space, giving rise to a continuous family of classical ground states. Further, the CN-ground states have a correspondence with dimer coverings and with self avoiding walks on a honeycomb lattice. The zero point energy of our spin wave theory picks out a subset from a continuous family of classically degenerate states as the quantum ground states; the number of these states also grows exponentially with N. In the second part, we present some exact results. For arbitrary spin-S, we show that localized Z_2 flux excitations are present by constructing plaquette operators with eigenvalues \pm 1 which commute with the Hamiltonian. This set of commuting plaquette operators leads to an exact vanishing of the spin-spin correlation functions, beyond nearest neighbor separation, found earlier for the spin-1/2 model [G. Baskaran, S. Mandal and R. Shankar, Phys. Rev. Lett. 98, 247201 (2007)]. We introduce a generalized Jordan-Wigner transformation for the case of general spin-S, and find a complete set of commuting link operators, similar to the spin-1/2 model, thereby making the Z_2 gauge structure more manifest. The Jordan-Wigner construction also leads, in a natural fashion, to Majorana fermion operators for half-integer spin cases and hard-core boson operators for integer spin cases, strongly suggesting the presence of Majorana fermion and boson excitations in the respective low energy sectors.

cond-mat.str-el↗

arXiv2008

Scattering of electrons from an interacting region

We address the problem of transmission of electrons between two noninteracting leads through a region where they interact (quantum dot). We use a model of spinless electrons hopping on a one-dimensional lattice and with an interaction on a single bond. We show that all the two-particle scattering states can be found exactly. Comparisons are made with numerical results on the time evolution of a two-particle wave packet and several interesting features are found for scattering. For N particles the scattering state is obtained by perturbation theory. For a dot connected to Fermi seas at different chemical potentials, we find an expression for the change in the Landauer current resulting from the interactions on the dot. We end with some comments on the case of spin-1/2 electrons.

cond-mat.mes-hall↗

arXiv2008

Theory of defect production in nonlinear quench across a quantum critical point

We study defect production in a quantum system subjected to a nonlinear power law quench which takes it either through a quantum critical or multicritical point or along a quantum critical line. We elaborate on our earlier work [D. Sen, K. Sengupta, S. Mondal, \prl 101, 016806 (2008)] and present a detailed analysis of the scaling of the defect density $n$ with the quench rate $τ$ and exponent $\al$ for each of the above-mentioned cases. We also compute the correlation functions for defects generated in nonlinear quenches through a quantum critical point and discuss the dependence of the amplitudes of such correlation functions on the exponent $\al$. We discuss several experimental systems where these theoretical predictions can be tested.

cond-mat.str-el↗

arXiv2008

Fully Symmetrized VB Based Technique for Solving Exchange Hamiltonians of Molecular Magnets

Generally, the first step in modeling molecular magnets involves obtaining the low-lying eigenstates of a Heisenberg exchange Hamiltonian which conserves total spin and belongs usually to a non-Abelian point group. In quantum chemistry, it has been a long standing problem to target a state which has definite total spin and also belongs to a definite irreducible representation of the point group. Many attempts have been made over years, but unfortunately these have not resulted in methods that are easy to implement, or even applicable to all point groups. Here we present a general technique which is a hybrid method based on VB basis and constant Ms basis, which is applicable to all types of point groups, easy to implement on computer. We illustrate the power of the method by applying it to the molecular magnetic system, Cu6Fe8, with cubic symmetry. We emphasize that our method is applicable to spin clusters with arbitrary site spins and is easily extended to Fermionic systems.

physics.chem-ph↗

arXiv2008

Defect generation in a spin-1/2 transverse XY chain under repeated quenching of the transverse field

We study the quenching dynamics of a one-dimensional spin-1/2 $XY$ model in a transverse field when the transverse field $h(=t/τ)$ is quenched repeatedly between $-\infty$ and $+\infty$. A single passage from $h \to - \infty$ to $h \to +\infty$ or the other way around is referred to as a half-period of quenching. For an even number of half-periods, the transverse field is brought back to the initial value of $-\infty$; in the case of an odd number of half-periods, the dynamics is stopped at $h \to +\infty$. The density of defects produced due to the non-adiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem and is generally found to vary as $1/\sqrtτ$ for large $τ$; however, the magnitude is found to depend on the number of half-periods of quenching. For two successive half-periods, the defect density is found to decrease in comparison to a single half-period, suggesting the existence of a corrective mechanism in the reverse path. A similar behavior of the density of defects and the local entropy is observed for repeated quenching. The defect density decays as $1/{\sqrtτ}$ for large $τ$ for any number of half-periods, and shows a increase in kink density for small $τ$ for an even number; the entropy shows qualitatively the same behavior for any number of half-periods. The probability of non-adiabatic transitions and the local entropy saturate to 1/2 and $\ln 2$, respectively, for a large number of repeated quenching.

cond-mat.stat-mech↗

arXiv2008

Defect production in non-linear quench across a quantum critical point

We show that the defect density $n$, for a slow non-linear power-law quench with a rate $τ^{-1}$ and an exponent $α>0$, which takes the system through a critical point characterized by correlation length and dynamical critical exponents $ν$ and $z$, scales as $n \sim τ^{-ανd/ (αzν+1)}$ [$n \sim (αg^{(α-1)/α}/τ)^{νd/(zν+1)}$], if the quench takes the system across the critical point at time $t=0$ [$t=t_0 \ne 0$], where $g$ is a non-universal constant and $d$ is the system dimension. These scaling laws constitute the first theoretical results for defect production in non-linear quenches across quantum critical points and reproduce their well-known counterpart for linear quench ($α=1$) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.

cond-mat.str-el↗

arXiv2008

A Theoretical Approach for Computing Magnetic Anisotropy in Single Molecule Magnets

We present a theoretical approach to calculate the molecular magnetic anisotropy parameters, $D_M$ and $E_M$ for single molecule magnets in any eigenstate of the exchange Hamiltonian, treating the anisotropy Hamiltonian as a perturbation. Neglecting inter-site dipolar interactions, we calculate molecular magnetic anisotropy in a given total spin state from the known single-ion anisotropies of the transition metal centers. The method is applied to $Mn_{12}Ac$ and $Fe_8$ in their ground and first few excited eigenstates, as an illustration. We have also studied the effect of orientation of local anisotropies on the molecular anisotropy in various eigenstates of the exchange Hamiltonian. We find that, in case of $Mn_{12}Ac$, the molecular anisotropy depends strongly on the orientation of the local anisotropies and the spin of the state. The $D_M$ value of $Mn_{12}Ac$ is almost independent of the orientation of the local anisotropy of the core $Mn(IV)$ ions. In the case of $Fe_8$, the dependence of molecular anisotropy on the spin of the state in question is weaker.

cond-mat.str-el↗

arXiv2008

Quasi-particle propagation in quantum Hall systems

We study various geometrical aspects of the propagation of particles obeying fractional statistics in the physical setting of the quantum Hall system. We find a discrete set of zeros for the two-particle kernel in the lowest Landau level; these arise from a combination of a two-particle Aharonov-Bohm effect and the exchange phase related to fractional statistics. The kernel also shows short distance exclusion statistics, for instance, in a power law behavior as a function of initial and final positions of the particles. We employ the one-particle kernel to compute impurity-mediated tunneling amplitudes between different edges of a finite-sized quantum Hall system and and find that they vanishes for certain strengths and locations of the impurity scattering potentials. We show that even in the absence of scattering, the correlation functions between different edges exhibits unusual features for a narrow enough Hall bar.

cond-mat.mes-hall↗

arXiv2008

Line junction in a quantum Hall system with two filling fractions

We present a microscopic model for a line junction formed by counter or co-propagating single mode quantum Hall edges corresponding to different filling factors. The ends of the line junction can be described by two possible current splitting matrices which are dictated by the conditions of both lack of dissipation and the existence of a linear relation between the bosonic fields. Tunneling between the two edges of the line junction then leads to a microscopic understanding of a phenomenological description of line junctions introduced some time ago. The effect of density-density interactions between the two edges is considered, and renormalization group ideas are used to study how the tunneling parameter changes with the length scale. This leads to a power law variation of the conductance of the line junction with the temperature. Depending on the strength of the interactions the line junction can exhibit two quite different behaviors. Our results can be tested in bent quantum Hall systems fabricated recently.

cond-mat.mes-hall↗

arXiv2008

Quench dynamics and defect production in the Kitaev and extended Kitaev models

We study quench dynamics and defect production in the Kitaev and the extended Kitaev models. For the Kitaev model in one dimension, we show that in the limit of slow quench rate, the defect density n \sim 1/\sqrtτ where 1/τis the quench rate. We also compute the defect correlation function by providing an exact calculation of all independent non-zero spin correlation functions of the model. In two dimensions, where the quench dynamics takes the system across a critical line, we elaborate on the results of earlier work [K. Sengupta, D. Sen and S. Mondal, Phys. Rev. Lett. 100, 077204 (2008)] to discuss the unconventional scaling of the defect density with the quench rate. In this context, we outline a general proof that for a d dimensional quantum model, where the quench takes the system through a d-m dimensional gapless (critical) surface characterized by correlation length exponent νand dynamical critical exponent z, the defect density n \sim 1/τ^{m ν/(z ν+1)}. We also discuss the variation of the shape and the spatial extent of the defect correlation function with the change of both the rate of quench and the model parameters and compute the entropy generated during such a quench process. Finally, we study the defect scaling law, entropy generation and defect correlation function of the two-dimensional extended Kitaev model.

cond-mat.stat-mech↗

arXiv2008

Exact results for quench dynamics and defect production in a two-dimensional model

We show that for a d-dimensional model in which a quench with a rate τ^{-1} takes the system across a d-m dimensional critical surface, the defect density scales as n \sim 1/τ^{mν/(zν+1)}, where νand z are the correlation length and dynamical critical exponents characterizing the critical surface. We explicitly demonstrate that the Kitaev model provides an example of such a scaling with d=2 and m=ν=z=1. We also provide the first example of an exact calculation of some multispin correlation functions for a two-dimensional model which can be used to determine the correlation between the defects. We suggest possible experiments to test our theory.

cond-mat.stat-mech↗

arXiv2007

Nonadiabatic charge pumping in a one-dimensional system of noninteracting electrons by an oscillating potential

Using a tight-binding model, we study one-parameter charge pumping in a one-dimensional system of non-interacting electrons. An oscillating potential is applied at one site while a static potential is applied in a different region. Using Floquet scattering theory, we calculate the current up to second order in the oscillation amplitude and exactly in the oscillation frequency. For low frequency, the charge pumped per cycle is proportional to the frequency and therefore vanishes in the adiabatic limit. If the static potential has a bound state, we find that such a state has a significant effect on the pumped charge if the oscillating potential can excite the bound state into the continuum states or vice versa. Finally, we use the equation of motion for the density matrix to numerically compute the pumped current for any value of the amplitude and frequency. The numerical results confirm the unusual effect of a bound state.

cond-mat.mes-hall↗

arXiv2007

Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field

We study the quantum dynamics of a one-dimensional spin-1/2 anisotropic XY model in a transverse field when the transverse field or the anisotropic interaction is quenched at a slow but uniform rate. The two quenching schemes are called transverse and anisotropic quenching respectively. Our emphasis in this paper is on the anisotropic quenching scheme and we compare the results with those of the other scheme. In the process of anisotropic quenching, the system crosses all the quantum critical lines of the phase diagram where the relaxation time diverges. The evolution is non-adiabatic in the time interval when the parameters are close to their critical values, and is adiabatic otherwise. The density of defects produced due to non-adiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem and is generally found to vary as $1/\sqrtτ$, where $τ$ is the characteristic time scale of quenching, a scenario that supports the Kibble-Zurek mechanism. Interestingly, in the case of anisotropic quenching, there exists an additional non-adiabatic transition, in comparison to the transverse quenching case, with the corresponding probability peaking at an incommensurate value of the wave vector. In the special case in which the system passes through a multi-critical point, the defect density is found to vary as $1/τ^{1/6}$. The von Neumann entropy of the final state is shown to maximize at a quenching rate around which the ordering of the final state changes from antiferromagnetic to ferromagnetic.

cond-mat.stat-mech↗