arXiv subjects

Satyaki Kar

Publications and source records attributed to Satyaki Kar.

26 records · Page 2Linked to original sources

arXiv2017

Magnons in a two dimensional transverse field XXZ model

The XXZ model on a square lattice in the presence of a transverse magnetic field is studied within the spin wave theory to investigate the resulting canted antiferromagnet. The small and large field regimes are probed separately both for easy-axis and easy-plane scenarios which reveal an unentangled factorized ground state at an intermediate value of the field. Goldstone modes are obtained for the field-free $XY$ antiferromagnet as well as for the isotropic antiferromagnet with field up to its saturation value. Moreover, for an easy-plane anisotropy, we find that there exists a non-zero field, where magnon degeneracy appears as a result of restoration of an U(1) sublattice symmetry and that, across that field, there occurs a magnon band crossing. For completeness, we then obtain the system phase diagram for $S=1/2$ via large scale quantum Monte Carlo simulations using the stochastic series expansion technique. Our numerical method is based on a quantization of spin along the direction of the applied magnetic field and does not suffer from a sign-problem, unlike comparable algorithms based on a spin quantization along the axis of anisotropy. With this formalism, we are also able to obtain powder averages of the transverse and longitudinal magnetizations, which may be useful for understanding experimental measurements on polycrystalline samples.

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arXiv2016

Two rate periodic protocol with dynamics driven through many cycles

We study the long time dynamics in closed quantum systems periodically driven via time dependent parameters with two frequencies $ω_1$ and $ω_2=r ω_1$. Tuning of the ratio $r$ there can unleash plenty of dynamical phenomena to occur. Our study includes integrable models like Ising and XY models in $d=1$ and Kitaev model in $d=1$ and $2$ and can also be extended to Dirac fermions in graphene. We witness the wave-function overlap or dynamic freezing to occur within some small/ intermediate frequency regimes in the $(ω_1 ,r)$ plane (with $r\ne0$) when the ground state is evolved through single cycle of driving. However, evolved states soon become steady with long driving and the freezing scenario gets rarer. We extend the formalism of adiabatic-impulse approximation for many cycle driving within our two-rate protocol and show the near-exact comparisons at small frequencies. An extension of the rotating wave approximation is also developed to gather an analytical framework of the dynamics at high frequencies. Finally we compute the entanglement entropy in the stroboscopically evolved states within the gapped phases of the system and observe how it gets tuned with the ratio $r$ in our protocol. The minimally entangled states are found to fall within the regime of dynamical freezing. In general, the results indicate that the entanglement entropy in our driven short-ranged integrable systems follow genuine non-area law of scaling and show a convergence (with a $r$ dependent pace) towards volume scaling behavior as the driving is continued for long time.

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arXiv2016

Tuning towards dynamic freezing using a two-rate protocol

We study periodically driven closed quantum systems where two parameters of the system Hamiltonian are driven with frequencies $ω_1$ and $ω_2=r ω_1$. We show that such drives may be used to tune towards dynamics induced freezing where the wavefunction of the state of the system after a drive cycle at time $T= 2π/ω_1$ has almost perfect overlap with the initial state. We locate regions in the $(ω_1 ,r)$ plane where the freezing is near exact for a class of integrable and a specific non-integrable model. The integrable models that we study encompass Ising and XY models in $d=1$, Kitaev model in $d=2$, and Dirac fermions in graphene and atop a topological insulator surface whereas the non-integrable model studied involves the experimentally realized one-dimensional (1D) tilted Bose-Hubbard model in an optical lattice. In addition, we compute the relevant correlation functions of such driven systems and describe their characteristics in the region of $(ω_1,r)$ plane where the freezing is near-exact. We supplement our numerical analysis with semi-analytic results for integrable driven systems within adiabatic-impulse approximation and discuss experiments which may test our theory.

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arXiv2015

Magnon dispersion and Single hole motion in 2D frustrated antiferromagnets with four-sublattice structures

We study a two dimensional spin-$\frac{1}{2}$ $J_1-J_2$ antiferromagnet in a square lattice using the linearized spin wave theory recognizing the 4-sublattice nature of the underlying magnetic lattice. Multiple magnon modes with optical and acoustic branches about the stable Neel ordered and double acoustic branches about the columnar reference states are obtained for small and large values of $λ(=J_2/J_1)$ respectively. An additional uniaxial anisotropy, for large $λ$, can lead to distinct spin gaps in such systems, as also witnessed experimentally. The single hole spectral behavior in a 2D $t-J_1-J_2$ model, for small frustration, is then calculated within the non-crossing approximation. Our results match fairly well with exact diagonalization results from a $4\times4$ cluster. Hole spectral features and their evolution with $λ$ resulting in "water-fall"-like smooth spectral weight transfer are discussed. Hole energy bands are identified and the corresponding energy-shift and reduction in width with spin-frustration are indicated.

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arXiv2015

Coexistence of long-range orders in a Bose-Holstein model

Exploring supersolidity in naturally occurring and artificially designed systems has been and will continue to be an area of immense interest. Here, we study how superfluid and charge-density-wave (CDW) states cooperate or compete in a minimal model for hard-core-bosons (HCBs) coupled locally to optical phonons: a two-dimensional Bose-Holstein model. Our study is restricted to the parameter regimes of strong HCB-phonon coupling and non-adiabaticity. We use Quantum Monte Carlo simulation (involving stochastic-series-expansion technique) to study phase transitions and to investigate whether we have homogeneous or phase-separated coexistence. The effective Hamiltonian involves, besides a nearest-neighbor hopping and a nearest-neighbor repulsion, sizeable double-hopping terms (obtained from second-order perturbation). At densities not far from half-filling, in the parameter regime where the double-hopping terms are non-negligible (negligible) compared to the nearest-neighbor hopping, we get checkerboard-supersolidity (phase separation) with CDW being characterized by ordering wavevector $\vec{Q}=(π,π)$.

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arXiv2013

Quasi-2D $J_1$-$J_2$ Antiferromagnet $Zn_2VO(PO_4)_2$ and its $Ti$-substituted Derivative - A Spin-wave Analysis

In this study, we present non-linear spin wave analysis of a quasi 2D spin-$\frac{1}{2}$ $J_1-J_2$ antiferromagnet at the parameter regime relevant for the recently studied compound $Zn_2VO(PO_4)_2$. We obtain the temperature dependence of the spin wave energy, susceptibility and magnetization using Green's function technique and Hartree-Fock factorization or Tyablikov's decoupling approximation. The comparison of our numerical results with the experimental findings is discussed. Magnetic structure factor is calculated and compared with powder neutron diffraction data. We also study the spin wave behavior of the compound $Zn_2Ti_{0.25}V_{0.75}O(PO_4)_2$ obtained by partial chemical substitution of $Ti$ at $V$ sites of the compound $Zn_2VO(PO_4)_2$ (Phys. Rev. B87, 054431). Due to the superlattice structure of the spin lattice, the substituted compound possess multiple spin wave modes. The spin wave analysis confirms the quasi-1D nature of the substituted system.

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arXiv2011

Hole spectral functions in lightly doped quantum antiferromagnets

We study the hole and magnon spectral functions as a function of hole doping in the two-dimensional (2D) t-J and t-t'-t"-J models working within the limits of the spin-wave theory, by linearizing the hole-spin-deviation interaction and by adapting the non-crossing approximation (NCA). We find that the staggered magnetization decreases rather rapidly with doping and it goes to zero at a few percent of hole concentration in both t-J and the t-t'-t"-J model. We find that with doping, the residue of the quasiparticle peak at G=(pi/2,pi/2) decreases rapidly with doping and the spectral function is in agreement with high resolution angle-resolved photo-emission spectroscopy (ARPES) studies of the copper-oxide superconductors. The observed large shift of the chemical potential inside the Mott gap is found to be a result of broadening of the quasiparticle peak. We find pockets centered at G, similar to those observed by quantum oscillation measurements, (i) with an elliptical shape with large eccentricity along the anti-nodal direction in the case of the t-J model, and (ii) with an almost circular shape in the case of the t-t'-t"-J model. We also find that the spectral intensity distribution in the doped antiferromagnet has a waterfall-like patten along the nodal direction of the Brillouin zone, a feature that is also seen in ARPES measurements.

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arXiv2008

Finite temperature spectral function of a hole in a quantum antiferromagnet and role of phonons

We study thermal broadening of the hole spectral function of the two-dimensional t-J model (and its extensions) within the non-crossing approximation with and without the contribution of optical phonons. We find that phonons at finite temperature broaden the lowest energy quasiparticle peak, however, the string excitations survive even for relatively strong electron-phonon coupling. Experimental angle resolved photo-emission spectroscopy(ARPES) results compare well with our calculations at finite temperature when we use strong electron-phonon coupling without any adhoc broadening. In addition, we have studied the role of vertex corrections and we find that their contribution allows us achieve the same overall agreement with the ARPES experimental results but using smaller values for the electron-phonon coupling.

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