arXiv subjects

Victor Mukherjee

Publications and source records attributed to Victor Mukherjee.

43 records · Page 3Linked to original sources

arXiv2011

Oscillating fidelity susceptibility near a quantum multicritical point

We study scaling behavior of the geometric tensor $χ_{α,β}(λ_1,λ_2)$ and the fidelity susceptibility $(χ_{\rm F})$ in the vicinity of a quantum multicritical point (MCP) using the example of a transverse XY model. We show that the behavior of the geometric tensor (and thus of $χ_{\rm F}$) is drastically different from that seen near a critical point. In particular, we find that is highly non-monotonic function of $λ$ along the generic direction $λ_1\simλ_2 = λ$ when the system size $L$ is bounded between the shorter and longer correlation lengths characterizing the MCP: $1/|λ|^{ν_1}\ll L\ll 1/|λ|^{ν_2}$, where $ν_1<ν_2$ are the two correlation length exponents characterizing the system. We find that the scaling of the maxima of the components of $χ_{αβ}$ is associated with emergence of quasi-critical points at $λ\sim 1/L^{1/ν_1}$, related to the proximity to the critical line of finite momentum anisotropic transition. This scaling is different from that in the thermodynamic limit $L\gg 1/|λ|^{ν_2}$, which is determined by the conventional critical exponents. We use our results to calculate the defect density following a rapid quench starting from the MCP and show that it exerts a step-like behavior for small quench amplitudes. Study of heat density and diagonal entropy density also show signatures of quasi-critical points.

cond-mat.stat-mech↗

arXiv2010

Adiabatic multicritical quantum quenches: Continuously varying exponents depending on the direction of quenching

We study adiabatic quantum quenches across a quantum multicritical point (MCP) using a quenching scheme that enables the system to hit the MCP along different paths. We show that the power-law scaling of the defect density with the rate of driving depends non-trivially on the path, i.e., the exponent varies continuously with the parameter $α$ that defines the path, up to a critical value $α= α_c$; on the other hand for $α\geq α_c$, the scaling exponent saturates to a constant value. We show that dynamically generated and {\it path($α$)-dependent} effective critical exponents associated with the quasicritical points lying close to the MCP (on the ferromagnetic side), where the energy-gap is minimum, lead to this continuously varying exponent. The scaling relations are established using the integrable transverse XY spin chain and generalized to a MCP associated with a $d$-dimensional quantum many-body systems (not reducible to two-level systems) using adiabatic perturbation theory. We also calculate the effective {\it path-dependent} dimensional shift $d_0(α)$ (or the shift in center of the impulse region) that appears in the scaling relation for special paths lying entirely in the paramagnetic phase. Numerically obtained results are in good agreement with analytical predictions.

cond-mat.stat-mech↗

arXiv2009

Defect production due to quenching through a multicritical point and along a gapless line

In this review, we study the quenching dynamics of a one-dimensional XY Hamiltonian in a transverse field under linear variation of different parameters of the Hamiltonian so that the system is driven through various critical points and gapless lines. It is observed that the density of defects falls off as a power law with the quenching rate $1/τ$ where the power law is determined by the dimensionality of the underlying lattice and the critical exponents associated with the quantum critical point as predicted by Kibble-Zurek scaling. However, we show that when the system is driven through a multicritical point or along a gapless line, Kibble Zurek scaling needs to be modified. We discuss generalized scaling forms of the defect density for the above two situations.

cond-mat.stat-mech↗

arXiv2009

Effects of interference in the dynamics of spin-1/2 transverse XY Chain driven periodically through quantum critical points

We study the effects of interference on the quenching dynamics of a one-dimensional spin 1/2 $XY$ model in the presence of a transverse field ($h(t)$) which varies sinusoidally with time as $h = h_0\cos{ωt}$, with $|t| \leq t_f = π/ω$. We also consider the situation where the magnetic field consists of an oscillatory as well as a linearly varying component, i.e., $h(t) = h_0\cos{ωt} + t/τ$. Our purpose is to estimate the defect density and the local entropy density in the final state if the system is initially prepared in its ground state. For a single crossing through the quantum critical point with $h = h_0\cos{ωt}$, the density of defects in the final state is calculated by mapping the dynamics to an equivalent Landau Zener problem by linearizing near the crossing point, and is found to vary as $\sqrtω$ in the limit of small $ω$. On the other hand, the local entropy density is found to attain a maximum as a function of $ω$ near a characteristic scale $ω_0$. Extending to the situation of multiple crossings, we show that the non-trivial interference effects of certain resonance modes solely contribute to the production of defects. Kink density as well as the diagonal entropy density show oscillatory dependence on the number of full cycles of oscillation. Finally, the inclusion of a linear term in the transverse field on top of the oscillatory component, results to a kink density which decreases continuously with $τ$ and $ω$. The entropy density shows monotonous growth with both $τ$ and $ω$, in sharp contrast to the situations studied earlier. We do also propose appropriate scaling relations for the defect density in above situations and compare the results with the numerical results obtained by integrating the Schrodinger equations.

cond-mat.stat-mech↗

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

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↗

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↗