arXiv subjects

Saptarshi Mandal

Publications and source records attributed to Saptarshi Mandal.

47 records · Page 3Linked to original sources

arXiv2019

Dipole-dipole interaction induced phases in Hydrogen-bonded squaric acid crystal

We study analytically the finite-temperature phase diagram of proton ordering of a quasi-two dimensional hydrogen-bonded system, namely the squaric acid crystal($\text{H}_2\text{C}_4\text{O}_4$). We take into account the four-spin interaction model at the zeroth order. Using an improvised loop algorithm within the Stochastic series expansion quantum monte carlo method, we find two distinct phases as we increase the temperature and magnetic-field. One of the phase is the $Π_f$, the phase with long range ferroelectric order and the other being an intermediate state with strong local correlations, i.e, a quantum liquid-like state $Π_{ql}$. The transition to $Π_{f}$ shows a very small anomalous peak in the specific heat with strong dependence of critical temperature on the strength of dipole-dipole interaction. The presence of the small peak is attributed to the absence of macroscopic degeneracy in the presence of dipole-dipole interaction and re-entrance of such degeneracy to some extent at small temperature. Though the degenerate ground state manifold is identical for a four-spin interaction or appropriate two-spin interaction model at zeroth order, we find that for the former case, the required strength of dipole-dipole interaction is quite larger to induce a ferroelectric phase. The work also presents an intricate connection of quantum fluctuation and thermal fluctuation in the presence of competing interaction with entropic effects.

cond-mat.str-el↗

arXiv2018

Quantum theory of spin waves for Helical ground states in Hollandite lattice

We perform spin wave analysis of classical ground states of a model Hamiltonian proposed earlier(Phys. Rev. B {\bf 90}, 104420(2014)) for $α-MnO_2$ compounds. It is known that the phase diagram of the Hollandite lattice (lattice of $α-MnO_2$ compounds) consists of four different Helical phases(FH, A2H, C2H, CH phase) in the space of model parameters $J_1,~J_2,~J_3$. The spin wave dispersion shows presence of gapless mode which interpolates between quadratic to linear depending on phases and values of $J_i$'s. In most cases, the 2nd lowest mode shows the existence of a roton minima mainly from $X$ to $M$ and $M$ to $Z$ path. Few higher modes also show roton minima. Each helical phase has its characteristic traits which can be used to determine the phases itself. The analytical expressions of eigenmodes at high symmetry points are obtained which can be utilized to extract the values of $J_i$'s. Density of states, specific heat and susceptibilities at low temperature has been studied within spin wave approximation. The specific heat shows departure from $T^{1.5(3)}$ dependence found in three dimensional unfrustrated ferromagnetic(anti-ferromagnetic) system which seems to be the signature of incommensurate helical phase. The parallel susceptibility is maximum for FH phase and minimum for CH phase at low temperature. The perpendicular susceptibility is found to be independent of temperature at very low temperature. Our study can be used to compare experimental results on magnon spectrum, elastic neutron scattering, and finite temperature properties mentioned above for clean $α-MnO_2$ system

cond-mat.str-el↗

arXiv2018

Classical ground states, spin-wave and PCUT analysis of $\rm H_2SQ$ system

We study an organic Hydrogen bonded material $\rm{H_2SQ}$ analytically and map out the phase diagram as well as low energy excitations in the relevant parameter space. At zeroth order the dynamics is governed by plaquette interaction (product of $σ_z$ over a plaquette) which defines a $Z_2$ gauge theory and a deconfinement phase satisfying "ice rules". The system is studied under additional interactions such as an external Zeeman field (with strength $K$) in $x$-direction, a inter-molecular interaction (with strength $J_1$) and a dipole-dipole interaction with strength $J_2$ such that $K>J_1>J_2$. The effect of dipole-dipole interaction removes the local $Z_2$ symmetry and gives rise to four global degenerate states with Ferroeletric order. Using meanfield analysis we chart out the phase diagram for classical version of the model and find $K_c$ which defines the transition from disordered phase to ordered phase in $J_1, K$ plane for various values of $J_2$. We find that presence of $J_1$ and $J_2$ tends to stabilize the deconfined phases. Over the classical ground states we perform spin-wave analysis and surprisingly find that quantum fluctuations does not remove the classical degeneracy at all at quadratic level. The spin-wave spectrum is found for the four global degenerate ground states which shows both gapped spectrum and gapless spectrum (near the vicinity of CDT transition) for $J_2=0$. However for $J_2$ finite, the spectrum is always gapped. We perform PCUT analysis to improve the results of spin-wave analysis and calculate ground state energy and one particle dispersion and gap at high symmetry point. Using this we draw the phase boundary between confined and deconfined phase in the $K-J_1$ plane. The effect of $J_2$ is also discussed in the resulting phase boundary.

cond-mat.str-el↗

arXiv2016

Entanglement and Majorana edge states in the Kitaev model

We investigate the von Neumann entanglement entropy and Schmidt gap in the ground state of the Kitaev model on the honeycomb lattice for square and cylindrical subsystems. We find that, for both the subsystems, the free-fermionic contribution to the entanglement entropy $S_E$ exhibits signatures of the phase transitions between the gapless and gapped phases. However, we find that $S_E$ does not show an expected monotonic behaviour as a function of the coupling $J_z$ between the suitably defined one-dimensional chains within the gapless phase for either geometry; moreover the system generically reaches a point of minimum entanglement within the gapless phase before the entanglement saturates or increases again until the gapped phase is reached. This may be attributed to the competition between the nearest neighbour correlation functions of the $x-x$ and $z-z$ bonds, and to the onset of gapless $\vec{k}$-modes in the bulk spectrum. On the other hand $S_E$ always monotonically varies with $J_z$ in the gapped phase independent of the subregion size or shape. Finally, further confirming the Li-Haldane conjecture, we find that the Schmidt gap $Δ$ defined from the entanglement spectrum also signals the topological transitions but only if there are corresponding zero energy Majorana edge states that simultaneously appear or disappear across the transitions. We analytically corroborate some of our results on entanglement entropy, Schmidt gap and the bulk-edge correspondence using perturbation theory.

cond-mat.str-el↗

arXiv2013

Study of unconventional superfluid phases and the phase dynamics in spin-orbit coupled bose system

We study the phase distribution and its dynamics in spin-orbit coupled two component ultracold Bosons for finite size system. Using an inhomogeneous meanfield analysis we demonstrate how phase distribution evolves as we tune the spin-orbit coupling $γ$ and $t$, the spin-independent hopping. For $t>>γ$ we find the homogeneous superfluid phase. As we increase $γ$, differences in the phases of the order parameter grows leading to twisted superfluid phase. For $t \sim γ$ competing orderings in the phase distribution is observed. At large $γ$ limit a Ferro-Magnetic stripe ordering appears along the diagonal. We explain that this is due to the frustration bought in by the spin-orbit interaction. Isolated vortex formation is also shown to appear. We also investigate the possible collective modes. In deep superfluid regime we derive the equation of motion for the phases following a semi-classical approximation. Imaginary frequencies indicating the damped modes are seen to appear and the dynamics of lowest normal modes are discussed.

cond-mat.str-el↗

arXiv2012

Superfluid-Insulator transition of two-species bosons with spin-orbit coupling

Motivated by recent experiments [Y.J. Lin {\it et al.}, Nature {\bf 471}, 83 (2011)], we study Mott phases and superfluid-insulator (SI) transitions of two-species ultracold bosonic atoms in a two-dimensional square optical lattice with nearest neighbor hopping amplitude $t$ in the presence of a spin-orbit coupling characterized by a tunable strength $γ$. Using both strong-coupling expansion and Gutzwiller mean-field theory, we chart out the phase diagrams of the bosons in the presence of such spin-orbit interaction. We compute the momentum distribution of the bosons in the Mott phase near the SI transition point and show that it displays precursor peaks whose position in the Brillouin zone can be varied by tuning $γ$. Our analysis of the critical theory of the transition unravels the presence of unconventional quantum critical points at $t/γ=0$ which are accompanied by emergence of an additional gapless mode in the critical region. We also study the superfluid phases of the bosons near the SI transition using a Gutzwiller mean-field theory which reveals the existence of a twisted superfluid phase with an anisotropic twist angle which depends on $γ$. Finally, we compute the collective modes of the bosons and point out the presence of reentrant SI transitions as a function of $γ$ for non-zero $t$. We propose experiments to test our theory.

cond-mat.str-el↗

arXiv2011

RVB gauge theory and the Topological degeneracy in the Honeycomb Kitaev model

We relate the Z$_2$ gauge theory formalism of the Kitaev model to the SU(2) gauge theory of the resonating valence bond (RVB) physics. Further, we reformulate a known Jordan-Wigner transformation of Kitaev model on a torus in a general way that shows that it can be thought of as a Z$_2$ gauge fixing procedure. The conserved quantities simplify in terms of the gauge invariant Jordan-Wigner fermions, enabling us to construct exact eigen states and calculate physical quantities. We calculate the fermionic spectrum for flux free sector for different gauge field configurations and show that the ground state is four-fold degenerate on a torus in thermodynamic limit. Further on a torus we construct four mutually anti-commuting operators which enable us to prove that all eigenstates of this model are four fold degenerate in thermodynamic limit.

cond-mat.str-el↗

arXiv2011

Topological excitations in three dimensional Kitaev model

We study the excitations in a three dimensional version of Kitaev's spin-1/2 model on the honeycomb lattice introduced by the present authors recently. The gapped phase of the system is analyzed using a low energy effective Hamiltonian which is defined on the diamond lattice and consists of plaquette operators. The excitations of the effective Hamiltonian form loops in an embedded lattice. The elementary excitations, which are the shortest loops, are fermions. Moreover, the excitations obey nontrivial braiding rules: when a fermion winds through a loop, the wave function acquires a phase $π$.

cond-mat.str-el↗

arXiv2009

High temperature expansion, Virial coefficients and Exclusion statistics

We follow the generalisation of exclusion statistics to infinite dimensional Hilbert space as envisaged in Phys. Rev. Lett. {\bf{72}}, 3629, 1994. We reproduce the third virial coefficients at leading order for single species of anionic gas and 2nd mixed virial coefficients for multicomponent anionic gas. We argue that this particular method can be useful in determining definition of mutual exclusion statistics. We demonstrate this by taking high temperature expansion of two particle partition function of well known systems and show that it follows Haldane's definition of exclusion statistics. We also discuss equilibrium particle distributions at thermodynamic limit.

cond-mat.other↗

arXiv2009

Exactly solvable Kitaev model in three dimensions

We introduce a spin-1/2 model in three dimensions which is a generalization of the well-known Kitaev model on a honeycomb lattice. Following Kitaev, we solve the model exactly by mapping it to a theory of non-interacting fermions in the background of a static Z_2 gauge field. The phase diagram consists of a gapped phase and a gapless one, similar to the two-dimensional case. Interestingly, unlike in the two-dimensional model, in the gapless phase the gap vanishes on a contour in the k space. Furthermore, we show that the flux excitations of the gauge field, due to some local constraints, form loop like structures; such loops exist on a lattice formed by the plaquettes in the original lattice and is topologically equivalent to the pyrochlore lattice. Finally, we derive a low-energy effective Hamiltonian that can be used to study the properties of the excitations in the gapped phase.

cond-mat.mes-hall↗

arXiv2007

Exact results for spin dynamics and fractionization in the Kitaev Model

We present certain exact analytical results for dynamical spin correlation functions in the Kitaev Model. It is the first result of its kind in non-trivial quantum spin models. The result is also novel: in spite of presence of gapless propagating Majorana fermion excitations, dynamical two spin correlation functions are identically zero beyond nearest neighbor separation, showing existence of a gapless but short range spin liquid. An unusual, \emph{all energy scale fractionization}of a spin -flip quanta, into two infinitely massive $π$-fluxes and a dynamical Majorana fermion, is shown to occur. As the Kitaev Model exemplifies topological quantum computation, our result presents new insights into qubit dynamics and generation of topological excitations.

cond-mat.str-el↗