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arXiv:1601.04851 · Physical review. E

Tuning the presence of dynamical phase transitions in a generalized XY spin chain

Uma Divakaran, Shraddha Sharma, Amit Dutta

Published May 18, 2016• 63 citations
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Abstract

We study an integrable spin chain with three spin interactions and the staggered field $(\ensuremath{\lambda})$ while the latter is quenched either slowly [in a linear fashion in time $(t)$ as $t/\ensuremath{\tau}$, where $t$ goes from a large negative value to a large positive value and $\ensuremath{\tau}$ is the inverse rate of quenching] or suddenly. In the process, the system crosses quantum critical points and gapless phases. We address the question whether there exist nonanalyticities [known as dynamical phase transitions (DPTs)] in the subsequent real-time evolution of the state (reached following the quench) governed by the final time-independent Hamiltonian. In the case of sufficiently slow quenching (when $\ensuremath{\tau}$ exceeds a critical value ${\ensuremath{\tau}}_{1})$, we show that DPTs, of the form similar to those occurring for quenching across an isolated critical point, can occur even when the system is slowly driven across more than one critical point and gapless phases. More interestingly, in the anisotropic situation we show that DPTs can completely disappear for some values of the anisotropy term $(\ensuremath{\gamma})$ and $\ensuremath{\tau}$, thereby establishing the existence of boundaries in the $(\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\tau})$ plane between the DPT and no-DPT regions in both isotropic and anisotropic cases. Our study therefore leads to a unique situation when DPTs may not occur even when an integrable model is slowly ramped across a QCP. On the other hand, considering sudden quenches from an initial value ${\ensuremath{\lambda}}_{i}$ to a final value ${\ensuremath{\lambda}}_{f}$, we show that the condition for the presence of DPTs is governed by relations involving ${\ensuremath{\lambda}}_{i},{\ensuremath{\lambda}}_{f}$, and $\ensuremath{\gamma}$, and the spin chain must be swept across $\ensuremath{\lambda}=0$ for DPTs to occur.

DOI
10.1103/physreve.93.052133

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It is well known that the dynamics of a quantum system is always nonadiabatic in passage through a quantum critical point and the defect density in the final state following a quench shows a power-law scaling with the rate of quenching. However, we propose here a possible situation where the dynamics of a quantum system in passage across quantum critical regions is adiabatic and the defect density decays exponentially. This is achieved by incorporating additional interactions which lead to quantum critical behavior and gapless phases but do not participate in the time evolution of the system. To illustrate the general argument, we study the defect generation in the quantum critical dynamics of a spin-1/2 anisotropic quantum XY spin chain with three spin interactions and a linearly driven staggered magnetic field.
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We investigate the nonequilibrium dynamics induced by a finite-time linear quench in the XYXYXY chain. Initially, we examine the dynamical quantum phase transition (DQPT-LE), characterized by the nonanalytic behavior of the Loschmidt amplitude. We find distinct behaviors of DQPT-LEs during and following the ramp. Following the ramp, the ramp crossing the critical point hc{h}_{c}hc​ is the sufficient condition for the occurrence of DQPT-LE, but it is not during the ramp. Through adiabatic-impulse-adiabatic (AIA) approximation analysis, we establish that adequate distancing from the critical point is crucial for DQPT-LE manifestation during the ramp, elucidating the absence of DQPT-LE as the ramp gets faster. Additionally, we explore another type of dynamical phase transition (DQPT-OP), describing the long-term relaxation behavior of the order parameter. Our finding indicates that the asymptotic behavior of the time-dependent part induced by the linear quench is equivalent to that following a sudden quench, i.e., the time-dependent part exhibits power-law decays of $\ensuremath{\sim}{t}^{\ensuremath{-}3/2}$ and $\ensuremath{\sim}{t}^{\ensuremath{-}1/2}$ for the ramp to the commensurate and incommensurate phases, respectively. Moreover, we also delve into the steady part, which showcases nonanalytic singularities at the critical point.