arXiv subjects

Monalisa Singh Roy

Publications and source records attributed to Monalisa Singh Roy.

6 recordsLinked to original sources

arXiv2024

Universal scaling of quantum caustics in the dynamics of interacting particles

Recent theoretical studies have predicted the existence of caustics in many-body quantum dynamics, where they manifest as extended regions of enhanced probability density that obey temporal and spatial scaling relations. Focusing on the transverse-field Ising model, we investigate the dynamics initiated by a local quench in a spin chain, resulting in outward-propagating excitations that create a distinct caustic pattern. We calculate the scaling of the first two maxima of the interference fringes dressing the caustic, finding a universal exponent of 2/3, associated with an Airy function catastrophe. We demonstrate that this property is universal in the entire paramagnetic phase of the model, and starts varying at the quantum phase transition (QPT). This robust scaling persists even under perturbations that break the integrability of the model. We additionally explore the effect of boundary conditions and find that open boundaries introduce significant edge effects, leading to complex interference patterns. Despite these edge-induced dynamics, the overall power-law scaling exponent remains robust. These findings highlight the potential of quantum caustics as a powerful diagnostic tool for QPTs, demonstrating resilience against integrability-breaking perturbations and boundary condition variations.

quant-ph↗

arXiv2021

Fulde-Ferrel-Larkin-Ovchinnikov phase in one dimensional Fermi gas with attractive interactions and transverse spin-orbit coupling

We examine the existence and characteristics of the exotic Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase in a one-dimensional Fermi gas with attractive Hubbard interactions, in the presence of spin-orbit coupling (SOC) and Zeeman field. We show that a robust FFLO phase can be created in the presence of attractive on-site interactions and Zeeman field, and that the addition of SOC suppresses the FFLO order and enhances the pair formation. In absence of SOC, the system shows four phases: Bardeen-Cooper-Schrieffer (BCS), FFLO, multi- mode pairing and fully polarized phases by tuning the Zeeman field h, and the quantum transition between these phases is discontinuous with respect to h. In the presence of SOC, the transition from the BCS to FFLO phase becomes continuous. We present a complete phase diagram of this model both in the presence and in the absence of SOC at quarter electron filling and also explore the effect of SOC on the FFLO phase.

cond-mat.quant-gas↗

arXiv2020

Fermion parity gap and exponential ground state degeneracy of the one-dimensional Fermi gas with intrinsic attractive interaction

We examine the properties of a one-dimensional (1D) Fermi gas with attractive intrinsic (Hubbard) interactions in the presence of spin-orbit coupling and Zeeman field by numerically computing the pair binding energy, excitation gap, and susceptibility to local perturbations using the density matrix renormalization group. Such a system can, in principle, be realized in a system of ultracold atoms confined in a 1D optical lattice. We note that, in the presence of spatial interfaces introduced by a smooth parabolic potential, the pair binding and excitation energy of the system decays exponentially with the system size, pointing to the existence of an exponential ground state degeneracy, and is consistent with recent works. However, the susceptibility of the ground state degeneracy of this number-conserving system to local impurities indicates that the energy gap vanishes as a power law with the system size in the presence of local perturbations. We compare this system with the more familiar system of an Ising antiferromagnet in the presence of a transverse field realized with Rydberg atoms and argue that the exponential splitting in the clean number-conserving 1D Fermi system is similar to a phase with only conventional order.

cond-mat.str-el↗

arXiv2020

Tunneling density of states in a Y junction of Tomonaga-Luttinger liquid wires: A density matrix renormalization group study

It is well known that the pristine bulk of an interacting one-dimensional system in Tomonaga-Luttinger liquid (TLL) phase shows power law suppression of quasi-particle tunneling amplitude for all values of TLL parameter $g$, in the zero energy limit. We perform a density matrix renormalization group (DMRG) study of a fully symmetric Y junction of TLL wires and observe an anomalous enhancement of the tunneling density of states (TDOS) in the vicinity of the junction for both (a) interacting bosons case and (b) interacting fermions case, when $g>1$. We also observe suppression of TDOS for $g<1$ for both bosonic and fermionic cases. We find that the TDOS enhancements follow different power laws for bosonic and fermionic cases which suggests that these represent distinct fixed points, owing to statistical correlations which play an important role at the Y junction. Analysis of static conductance for the junction indicates that the fixed point for $1<g<3$ resembles the mysterious $M$ fixed point of Y junction predicted by Oshikawa, Chamon, and Affleck [J. Stat. Mech. P02008 (2006)]. We also show that the TDOS enhancement spans over a length scale of $\propto ω^{-1}$ from the junction, for $1<g<3$.

cond-mat.str-el↗

arXiv2020

Modeling the spin-Peierls transition of spin-$1/2$ chains with correlated states: $J_1-J_2$ model, CuGeO$_3$ and TTF-CuS$_4$C$_4$(CF$_3$)$_4$

The spin-Peierls transition at $T_{SP}$ of spin-$1/2$ chains with isotropic exchange interactions has previously been modeled as correlated for $T > T_{SP}$ and mean field for $T < T_{SP}$. We use correlated states throughout in the $J_1-J_2$ model with antiferromagnetic exchange $J_1$ and $J_2 = αJ_1$ between first and second neighbors, respectively, and variable frustration $0 \leq α\leq 0.50$. The thermodynamic limit is reached at high $T$ by exact diagonalization of short chains and at low $T$ by density matrix renormalization group calculations of progressively longer chains. In contrast to mean field results, correlated states of 1D models with linear spin-phonon coupling and a harmonic adiabatic lattice provide an internally consistent description in which the parameter $T_{SP}$ yields both the stiffness and the lattice dimerization $δ(T)$. The relation between $T_{SP}$ and $Δ(δ,α)$, the $T = 0$ gap induced by dimerization, depends strongly on $α$ and deviates from the BCS gap relation that holds in uncorrelated spin chains. Correlated states account quantitatively for the magnetic susceptibility of TTF-CuS$_4$C$_4$(CF$_3$)$_4$ crystals ($J_1 = 79$ K, $α= 0$, $T_{SP} = 12$ K) and CuGeO$_3$ crystals ($J_1 = 160$ K, $α= 0.35$, $T_{SP} = 14$ K). The same parameters describe the specific heat anomaly of CuGeO$_3$ and inelastic neutron scattering. Modeling the spin-Peierls transition with correlated states exploits the fact that $δ(0)$ limits the range of spin correlations at $T = 0$ while $T > 0$ limits the range at $δ= 0$.

cond-mat.str-el↗

arXiv2017

Characterization of Majorana-Ising phase transition in a helical liquid system

We map an interacting helical liquid system, coupled to an external magnetic field and s-wave superconductor, to an XYZ spin system, and it undergoes Majorana-Ising transition by tuning of parameters. In the Majorana state, lowest excitation gap decays exponentially with system size, and the system has degenerate ground state in the thermodynamic limit. On the contrary, the gap opens in the Ising phase even in the thermodynamic limit. We also study other criteria to characterize the transition, such as edge spin correlation with its neighbor $C(r=1)$, local susceptibility $χ_i$, superconducting order parameter of edge spin $P(r=1)$, and longitudinal structure factor $S(k)$. The ground state degeneracy and three other criteria lead to the same critical value of parameters for Majorana-Ising phase transition in the thermodynamic limit. We study, for the first time, the entanglement spectrum of the reduced density matrix of the helical liquid system. The system shows finite Schmidt gap and non-degeneracy of the entanglement spectrum in the Ising limit. The Schmidt gap closes in the Majorana state, and all the eigenvalues are either doubly or multiply degenerate.

cond-mat.str-el↗