arXiv subjects

V. Subrahmanyam

Publications and source records attributed to V. Subrahmanyam.

At least 19 recordsLinked to original sources

arXiv2025

Quantum correlations in a cluster spin model with three-spin interactions

An exactly solvable cluster spin model with three-spin interaction couplings J_x (for XZX spin components) and J_y (for YZY spin components) in the presence of a transverse magnetic field $h$ for a spin chain is investigated. For $h=0$, and with only one nonzero interaction strength, the ground state is the cluster state. Through the Jordan-Wigner fermion mapping, the odd sites and the even sites form two separate transverse-XY chains, connected only through the boundary terms. Consequently, all measures of quantum correlations for nearest neighbour spins, the concurrence, the quantum mutual information and the quantum discord are all zero in the ground state. The dynamics is spin conserving for J_y=J_x, exhibiting a line of critical points for |h/J_x| < 2, with an uncorrelated direct product ground state for |h/J_x|>2. There are several quantum critical points in the parameter space, with multi-fold degenerate ground states. The magnetisation and the global entanglement measure exhibit strong singular features for the spin conserving case. The next-neighbour quantum correlation measures are investigated analytically, which exhibit singular features in the vicinity of degeneracy critical points. The $J_y$- and $h$- derivatives of the concurrence exhibit singular peak behaviour near the degeneracy critical points, except in the spin conserving case where the derivatives are zero.

quant-ph↗

arXiv2022

Transmission across non-Hermitian $\mathcal{PT}$-symmetric quantum dots and ladders

A non-Hermitian region connected to semi-infinite Hermitian lattices acts either as a source or as a sink and the probability current is not conserved in a scattering typically. Even a $\mathcal{P}\mathcal{T}$-symmetric region that contains both a source and a sink does not lead to current conservation plainly. We propose a model and study the scattering across a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric two-level quantum dot~(QD) connected to two semi-infinite one-dimensional lattices in a special way so that the probability current is conserved. Aharonov-Bohm type phases are included in the model, which arise from magnetic fluxes ($\hbarϕ_{L} /e,~\hbarϕ_{R} /e$) through two loops in the system. We show that when $ϕ_L=ϕ_R$, the probability current is conserved. We find that the transmission across the QD can be perfect in the $\mathcal{P}\mathcal{T}$-unbroken phase (corresponding to real eigenenergies of the isolated QD) whereas the transmission is never perfect in the $\mathcal{P}\mathcal{T}$-broken phase (corresponding to purely imaginary eigenenergies of the QD). The two transmission peaks have the same width only for special values of the fluxes (being odd multiples of $π\hbar/2e$). In the broken phase, the transmission peak is surprisingly not at zero energy. We give an insight into this feature through a four-site toy model. We extend the model to a $\mathcal{P}\mathcal{T}$-symmetric ladder connected to two semi-infinite lattices. We show that the transmission is perfect in unbroken phase of the ladder due to Fabry-Pérot type interference, that can be controlled by tuning the chemical potential. In the broken phase of the ladder, the transmission is substantially suppressed.

cond-mat.mes-hall↗

arXiv2022

Information scrambling and redistribution of quantum correlations through dynamical evolution in spin chains

We investigate the propagation of local bipartite quantum correlations, along with the tripartite mutual information to characterize the information scrambling through dynamical evolution of spin chains. Starting from an initial state with the first pair of spins in a Bell state, we study how quantum correlations spread to other parts of the system, using different representative spin Hamiltonians, viz. the Heisenberg Model, a spin-conserving model, the transverse-field XY model, a non-conserving but integrable model, and the kicked Harper model, a spin conserving but nonintegrable model. We show that the local correlations spread consistently in the case of spin-conserving dynamics in both integrable and nonintegrable cases, with a strictly nonnegative tripartite mutual information. In contrast, in the case of non-conserving dynamics, tripartite mutual information is negative and local pair correlations do not propagate.

quant-ph↗

arXiv2022

Loschmidt echo and Momentum Distribution in a Kitaev Spin Chain

We investigate the Loschmidt echo in a one-dimensional spin chain having Kitaev-type interaction in constant and kicked magnetic fields. The Loschmidt echo for the initial states having different magnon excitations shows long-time revivals for smaller chains and has short-time revival peaks for the longer chains. The system near the critical point shows peculiarly long-time revival peaks of the Loschmidt echo for relatively larger chains. The presence of a magnon in the initial state affects the Loschmidt echo revival peaks. The momentum distribution function exhibits maxima for a few momenta that are associated with the momentum of the magnon excitation present in the initial states. The probability maxima decay as O(1/N ) with the system size. For the Hamiltonian with kicked magnetic fields, the Loschmidt echo depends on the kick period. For a special kick period, the Loschmidt echo shows no evolution at all irrespective of the system size.

quant-ph↗

arXiv2018

Loschmidt echo of local dynamical processes in integrable and non integrable spin chains

The Loschmidt echo is investigated to track the effect of the local QDP. It is also quite sensitive to whether the background dynamics is integrable or not. For the integrable case, viz. the Heisenberg model, the Loschmidt echo depends on the parameters operators corresponding to the QDP as well as the time of QDP. The probability of reviving the system to its initial state is higher for incoherent QDPs occurring at large time intervals. Whereas each time coherent QDP occurs certain probability of reviving the state is always lost. For For the non-integrable case, viz. a kicked Harper model, it exhibits a decaying behaviour when contrasted with integrable dynamics. The decay rate is slower when the corresponding classical Hamiltonian is non chaotic. The Loschmidt echo also distinguishes the integrable and the nonintegrable dynamics when a QDP occurs.

quant-ph↗

arXiv2018

Interference of the signal from a local dynamical process with the quantum state propagation in spin chains

The effect of a local instantaneous quantum dynamical process (QDP), either unitary or non-unitary, on the quantum state transfer through a unitary Hamiltonian evolution is investigated for both integrable and non-integrable dynamics. There are interference effects of the quantum state propagation and the QDP signal propagation. The state transfer fidelity is small for further sites, from the site where the information is coded, indicating a finite speed for the propagation of the quantum correlation. There is a small change in the state transfer fidelity for the case of non- unitary QDP intervening the background unitary dynamics. In the case of unitary QDP, the change is more pronounced, with a substantial increase in the fidelity for appropriate sites and times. For the non-integrable case, viz. a kicked Harper model, the state transfer fidelity is quite large for further sites for short times, indicating a finite speed for the propagation of the quantum correlation cannot be defined.

quant-ph↗

arXiv2018

Quantum correlations and entanglement in a Kitaev-type spin chain

The entanglement and quantum correlation measures have been investigated for the ground state of a spin chain with a Kitaev-type exchange interactions on alternating bonds, along with a transverse magnetic field. There is a macroscopic degeneracy in the ground state for zero magnetic field, implying a quantum critical point. But peculiarly in this model, the entanglement measures do not show any singular behavior in the vicinity of the critical point, as seen in the transverse Ising model ground state and related models. We have investigated different correlation measures analytically, that have been used for many solvable spin systems to track a quantum critical point. We compute the pair concurrence measure of entanglement, the pair quantum discord to track the quantum correlations, and a global entanglement measure and a multi-species entanglement measure to investigate multi-party entanglement, both analytically and numerically. The nearest-neighbor concurrence shows a peak structure as a function of magnetic field, near the critical point, for various values of the ratio of interaction strengths, but its derivative does not show a singular behavior close to the critical point. A similar behavior is shown by the quantum discord and the global entanglement. The multi-species entanglement shows the most-pronounced signature of the critical point, in its first-order derivative, though the entanglement and its derivatives have a smooth behavior in the critical region.

quant-ph↗

arXiv2017

Remotely detecting the signal of a local decohering process in spin chains

We study the dynamics of a one dimensional quantum spin chain evolving from unentangled or entangled initial state. At a given instant of time a quantum dynamical process (ex. measurement) is performed on a single spin at one end of the chain, decohering the system. Through the further unitary evolution, a signal propagates in the spin chain, which can be detected from a measurement on a different spin at later times. From the dynamical unitary evolution of the decohered state from the epoch time, it is possible to detect the occurrence of the dynamical process. The propagation of the signal for the dynamical process, and the speed of the signal are investigated for various spin models, viz. using the Ising, Heisenberg, and the transverse-XY dynamics.

quant-ph↗

arXiv2016

Intrinsic upper bound on two-qubit polarization entanglement predetermined by pump polarization correlations in parametric down-conversion

We study how one-particle correlations transfer to manifest as two-particle correlations in the context of parametric down-conversion (PDC), a process in which a pump photon is annihilated to produce two entangled photons. We work in the polarization degree of freedom and show that for any two-qubit generation process that is both trace-preserving and entropy-nondecreasing, the concurrence $C(ρ)$ of the generated two-qubit state $ρ$ follows an intrinsic upper bound with $C(ρ)\leq (1+P)/2$, where $P$ is the degree of polarization of the pump photon. We also find that for the class of two qubit states that is restricted to have only two non-zero diagonal elements such that the effective dimensionality of the two-qubit state is same as the dimensionality of the pump polarization state, the upper bound on concurrence is the degree of polarization itself, that is, $C(ρ)\leq P$. Our work shows that the maximum manifestation of two-particle correlations as entanglement is dictated by one-particle correlations. The formalism developed in this work can be extended to include multi-particle systems and can thus have important implications towards deducing the upper bounds on multi-particle entanglement, for which no universally accepted measure exists.

quant-ph↗

arXiv2016

Entanglement spectrum and block eigenvalue spacing distribution of correlated electron states

Entanglement spectrum of finite-size correlated electron systems are investigated using the Gutzwiller projection technique. The product of largest eigenvalue and rank of the block reduced density matrix, which is a measure of distance of the state from the maximally entangled state of the corresponding rank, is seen to characterise the insulator to metal crossover in the state. The fraction of distinct eigenvalues exhibits a `chaotic' behaviour in the crossover region, and it shows a `integrable' behaviour at both insulating and metallic ends. The integrated entanglement spectrum obeys conformal field theory (CFT) prediction at the metal and insulator ends, but shows a noticeable deviation from CFT prediction in the crossover regime, thus it can also track a metal-insulator crossover. A modification of the CFT result for the entanglement spectrum for finite size is proposed which holds in the crossover regime also. The adjacent level spacing distribution of unfolded non-zero eigenvalues for intermediate values of Gutzwiller projection parameter $g$ is the same as that of an ensemble of random matrices obtained by replacing each block of reduced density matrix by a random real symmetric Toeplitz matrix. It is strongly peaked at zero, with an exponential tail proportional to $e^{-(n/R)s}$, where $s$ is the adjacent level spacing, $n$ is number of distinct eigenvalues and $R$ is the rank of the reduced density matrix.

cond-mat.str-el↗

arXiv2014

Protocol using kicked Ising dynamics for generating states with maximal multipartite entanglement

We present a solvable model of iterating cluster state protocols that lead to entanglement production, between contiguous blocks, of 1 ebit per iteration. This continues till the blocks are maximally entangled at which stage an unravelling begins at the same rate till the blocks are unentangled. The model is a variant of the transverse field Ising model and can be implemented with CNOT and single qubit gates. The inter qubit entanglement as measured by the concurrence is shown to be zero for periodic chain realizations while for open boundaries there are very specific instances at which these can develop. Thus we introduce a class of simply produced states with very large multipartite entanglement content of potential use in measurement based quantum computing.

quant-ph↗

arXiv2014

Block entanglement and fluctuations in finite size correlated electron systems

The block entanglement entropy and fluctuations are investigated in one dimension in finite size correlated electron systems using the Gutzwiller wave function as a prototype correlated electron state. Entanglement entropy shows logarithmic divergence for all values of the correlation projection parameter $g$, as predicted by conformal field theories for critical systems, but the central charge requires finite size corrections. There is an infinite correlation length corresponding to correlation between same kinds of spins, for all values of $g$. A scaling form for the block entropy, as a function of $g$ and the system size $N$, is proposed which predicts a metal-insulator crossover at $N^{1/3} g\approx 0.24$. Bipartite fluctuations in the number of particles in a block, and the spin fluctuations also obey an approximate scaling. A relation is found between the block entropy and the bipartite spin fluctuations. Our results show some correspondence with an experiment on Ni nanochains.

cond-mat.str-el↗

arXiv2013

Block entropy for Kitaev-type spin chains in a transverse field

Block entanglement entropy in the ground state of a quantum spin chain is investigated. The spins have Kitaev-type nearest-neighbor interaction, of strength J_x or J_y, through either x or y components of the spins on alternating bonds, along with a transverse magnetic field h. An exact solution is obtained through Jordan-Wigner fermionization, and it exhibits a macroscopically degenerate ground state for h=0, and a non-degenerate ground state for nonzero h and for all interaction strengths. For a chain of N spins, we study the block entropy of a partition of L contiguous spins. The block entanglement entropy needs the eigenvalues of the 2^L-dimensional reduced density matrix. We employ an efficient method that reduces this problem to evaluating eigenvalues of a L-dimensional matrix, which enables us to calculate easily the block entanglement for large-N chains numerically. The entanglement entropy grows as log L, at the degeneracy point h=0, and only for J_x=J_y. For nonzero magnetic field, the entropy becomes independent of the size, thus obeying the area law. For unequal J_x and J_y, the block entropy shows a non-monotonic behavior for L<N/2.

quant-ph↗

arXiv2013

Distribution of quantum discord in Heisenberg Antiferromagnets

The quantum discord, which quantifies the amount of quantum correlations present between parts of a system, is investigated for antiferromagnetic spin systems. The discord for a pair of spins in the many-spin ground state is related to the diagonal and off-diagonal spin-spin correlation functions and the local magnetization. For isotropic and translationally invariant states, the discord is shown to be a function of the diagonal correlation function only. Thus, near a thermal/quantum critical point, the discord for a pair of spins shows long-range behavior, analogously of the correlation function. The discord exhibits a kink singularity as a function of the anisotropy parameter for the the ground state of the Heisenberg model, for both nearest-neighbor spins as well as for well-separated spins. The preferred measurement basis for the minimum conditional entropy, which determines the discord, changes discontinuously across the critical point. The conditional entropy distribution over all possible the measurement basis is investigated. For the isotropic model, the distribution is just a delta-function, whereas it has a twin-peak structure for anisotropic model. It is shown that the average value and the mean-square fluctuation of the conditional entropy also show a signature of the critical-point behavior.

quant-ph↗

arXiv2011

Slow dynamics of interacting antiferromagnetic nanoparticles

We study magnetic relaxation dynamics, memory and aging effects in interacting polydisperse antiferromagnetic NiO nanoparticles by solving a master equation using a two-state model. We investigate the effects of interactions using dipolar, Nearest-Neighbour Short-Range (NNSR) and Long-Range Mean-Field (LRMF) interactions. The magnetic relaxation of the nanoparticles in a time-dependent magnetic field has been studied using LRMF interaction. The size-dependent effects are suppressed in the ac-susceptibility, as the frequency is increased. We find that the memory dip, that quantifies the memory effect is about the same as that of non-interacting nanoparticles for the NNSR case. There is a stronger memory-dip for LRMF, and a weaker memory-dip for the dipolar interactions. We have also shown a memory effect in the Zero-field-cooled magnetization for the dipolar case, a signature of glassy behaviour, from Monte-Carlo studies.

cond-mat.mes-hall↗

arXiv2010

Macroscopic Multi-Species Entanglement near Quantum Phase Transitions

Multi-Species entanglement, defined for a many-particle system as the entanglement between different species of particles, is shown to exist in the thermodynamic limit of the system size going to infinity. This macroscopic entanglement, as it can exhibit singular behavior, is capable of tracking quantum phase transitions. The entanglement between up and down spins has been analytically calculated for the one-dimensional Ising model in a transverse magnetic field. As the coupling strength is varied, the first derivative of the entanglement shows a jump discontinuity and the second derivative diverges near the quantum critical point.

quant-ph↗

arXiv2010

Size-dependent magnetization fluctuations in NiO nanoparticles

The finite size and surface roughness effects on the magnetization of NiO nanoparticles is investigated. A large magnetic moment arises for an antiferromagnetic nanoparticle due to these effects. The magnetic moment without the surface roughness has a non-monotonic and oscillatory dependence on $R$, the size of the particles, with the amplitude of the fluctuations varying linearly with $R$. The geometry of the particle also matters a lot in the calculation of the net magnetic moment. An oblate spheroid shape particle shows an increase in net magnetic moment by increasing oblateness of the particle. However, the magnetic moment values thus calculated are very small compared to the experimental values for various sizes, indicating that the bulk antiferromagnetic structure may not hold near the surface. We incorporate the surface roughness in two different ways; an ordered surface with surface spins inside a surface roughness shell aligned due to an internal field, and a disordered surface with randomly oriented spins inside surface roughness shell. Taking a variational approach we find that the core interaction strength is modified for nontrivial values of $Δ$ which is a signature of multi-sublattice ordering for nanoparticles. The surface roughness scale $Δ$ is also showing size dependent fluctuations, with an envelope decay $Δ\sim R^{-1/5}$. The net magnetic moment values calculated using spheroidal shape and ordered surface are close to the experimental values for different sizes.

cond-mat.mes-hall↗

arXiv2009

Gobal entanglement and double occupancy in many-electron states

The entanglement in many-electron states is investigated using a global entanglement measure, viz. average site mixedness. We have examined metallic states of noninteracting electrons, Nagaoka and Gutzwiller states of strongly-correlated electrons, and superconducting states. Uncorrelated metallic states at half filling seem to maximize entanglement, as these states optimize the number of holes, the number of doubly-occupied sites. Entanglement is calculated explicitly for Gutzwiller-projected many-electron states in one dimension, which have less entanglement as double occupancy is inhibited in these states. Entanglement in superconducting states, which tend to promote double occupancy, is calculated as a function of the energy gap, and found to be lower than the metallic state entanglement. There is a possibility of a regime with a nonzero single-site concurrence depending on the energy gap.

quant-ph↗