Quench dynamics and defect production in the Kitaev and extended Kitaev models

Abstract

We study quench dynamics and defect production in the Kitaev and the extended Kitaev models. For the Kitaev model in one dimension, we show that in the limit of slow quench rate, the defect density n ϳ 1 / ͱ , where 1 / is the quench rate. We also compute the defect correlation function by providing an exact calculation of all independent nonzero spin correlation functions of the model. In two dimensions, where the quench dynamics takes the system across a critical line, we elaborate on the results of earlier work ͓K. Sengupta, D. Sen, and S. Mondal, Phys. Rev. Lett. 100, 077204 ͑2008͔͒ to discuss the unconventional scaling of the defect density with the quench rate. In this context, we outline a general proof that for a d-dimensional quantum model, where the quench takes the system through a d − m dimensional gapless ͑critical͒ surface characterized by correlation length exponent and dynamical critical exponent z, the defect density n ϳ 1 / m/͑z+1͒ . We also discuss the variation of the shape and spatial extent of the defect correlation function with both the rate of quench and the model parameters and compute the entropy generated during such a quenching process. Finally, we study the defect scaling law, entropy generation and defect correlation function of the two-dimensional extended Kitaev model.

Dynamical critical scaling and effective thermalization in quantum quenches: Role of the initial state

“…By now, the original KZS has been confirmed for a variety of models involving a regular isolated QCP [14][15][16][17][18] , and extensions have been introduced for more general adiabatic dynamics, including repeated 19 , non-linear 20 , and optimal 21 quench processes. In parallel, departures from the KZS predictions have emerged for more complex adiabatic scenarios, involving for instance quenches across either an isolated multicritical point (MCP) 20,[22][23][24][25] or non-isolated QCPs (that is, critical regions) [26][27][28][29] , as well as QPTs in infinitely-coordinated 30 , disordered 31 , and/or spatially inhomogeneous systems 12,32 . A main message that has emerged from the above studies is that, unlike in the standard KZS of Eq.…”

Compass models: Theory and physical motivations

“…In its simplest initial rendition (Brzezicki et al, 2007), this model is defined on a chain in which nearest neighbor interactions sequentially toggle between being of the τ x 2i τ x 2i+1 and τ y 2i+1 τ y 2i+2 variants as one proceeds along the chain direction for even/odd numbered bonds. Many aspects of this model have been investigated such as its quench dynamics (Divakarian and Dutta, 2009;Mondal et al, 2008). Such a system is, in fact, dual to the well-studied onedimensional transverse field Ising model, e.g., (Brzezicki et al, 2007;Eriksson and Johannesson, 2009;Nussinov and Ortiz, 2009b).…”

Topological quantum phase transition in the extended Kitaev spin model

“…For Hamiltonian (14), the ground-state energy is − k ε(k) and the ground-state |g obeys B † k B k |g = |g . The energy spectrum ε(k) is gapless [10] only when J x = J y + J z , or J y = J z + J x , or J z = J x + J y , which corresponds to the thick solid, dashed, and dotted lines in Fig.…”