Quenching dynamics of a quantum<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math>spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mstyle scriptlevel="1"><mml:mfrac bevelled="false"><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle></mml:math>chain in a transverse field

Mukherjee, Victor; Divakaran, Uma; Dutta, Amit; Sen, Diptiman

doi:10.1103/physrevb.76.174303

Cited by 157 publications

(192 citation statements)

References 30 publications

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“…Let us recall the quenching dynamics of the transverse XY spin chain discussed before [13,16]. When the system is quenched across the Ising or anisotropic critical line by linearly changing h or J x as t/τ, ∆ (k) vanishes at the critical point as ∆ (k) ∼ |k| yielding z 2 = z = 1; hence the generalized scaling form given in Eq.…”

Section: Quenching Through a Multicritical Pointmentioning

confidence: 99%

“…Evaluating the probability of a non-adiabatic transition for the mode k and integrating over the Brillouin zone, it can be shown that the density of defects in the final state following the anisotropic quenching is given by [16] …”

Section: And the New Hamiltonian Ismentioning

confidence: 99%

“…The meeting points of these two transition lines at h = ±(J x + J y ) and J x = J y are multicritical points. Let us initiate our discussions with two types of quenching schemes: (i) quenching the magnetic field h as t/τ which we call transverse quenching [11,13], and (ii) the quenching of the interaction J x as t/τ which is referred to as anisotropic quenching [16]. In the process of anisotropic quenching, the system can be made to cross the multicritical points A and B shown in the phase diagram.…”

Section: A Spin Model: Transverse and Anisotropic Quenchingmentioning

confidence: 99%

“…The Kibble-Zurek scaling has been verified in various exactly solvable spin models and systems of interacting bosons [4,13,16,17,11,5]; it has been generalized to quenching through a multicritical point [31], across a gapless phase [20,23], and along a gapless line [26,28], and to systems with quenched disorder [14], white noise [18], infinite-range interactions [27], and edge states [30]. Studies have also been made to estimate the defect density for quenching with a non-linear form [21], an oscillatory variation of an applied magnetic field [32] or under a reversal of the magnetic field [33].…”

Section: Introductionmentioning

confidence: 99%

“…The non-equilibrium dynamics of a quantum system when quenched very fast [3] or slowly across a quantum critical point [4,5] has attracted the attention of several groups recently. The possibility of experimental realizations of quantum dynamics in spin-1 Bose condensates [6] and atoms trapped in optical lattices [7,8] has led to an upsurge in studies of related theoretical models [3,4,5,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33].…”

mentioning

confidence: 99%

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Defect Production Due to Quenching Through a Multicritical Point and Along a Gapless Line

Divakaran

Mukherjee

Dutta

et al. 2010

Lecture Notes in Physics

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The exciting physics of quantum phase transitions has been explored extensively in the last few years [1,2]. The non-equilibrium dynamics of a quantum system when quenched very fast [3] or slowly across a quantum critical point [4,5] has attracted the attention of several groups recently. The possibility of experimental realizations of quantum dynamics in spin-1 Bose condensates [6] and atoms trapped in optical lattices [7,8] has led to an upsurge in studies of related theoretical models [3,4,5,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33].In this review, we concentrate on the dynamics of quantum spin chains swept across a quantum critical or multicritical point or along a gapless line by a slow (adiabatic) variation of a parameter appearing in the Hamiltonian of the system. Our aim is to find the scaling form of the density of defects (which, in our case, is the density of wrongly oriented spins) in the final state which is reached after the system is prepared in an initial ground state and then slowly quenched through a quantum critical point. The dynamics in the vicinity of a quantum critical point is necessarily non-adiabatic due to the divergence of the relaxation time of the underlying quantum system which forces the system to be infinitely sluggish; thus the system fails to respond to a change in a parameter of the Hamiltonian no matter how slow that rate of change may be! We first recall the Kibble-Zurek argument [34,35] which predicts a scaling form for the defect density following a slow quench through a quantum critical point. We assume that a parameter g of the Hamiltonian is varied in a linear fashion such that g − g c ∼ t/τ, where g = g c denotes the value of g at the quantum critical point and τ is the quenching time. Our interest is in the adiabatic limit, τ → ∞. The energy gap of the quantum Hamiltonian vanishes at the critical point as (g − g c ) νz whereas the relaxation time ξ τ , which is inverse of the gap, diverges at the critical point. It is clear that non-adiabaticity becomes important at a timet when the characteristic time scale of the quantum system (i.e., the relaxation time) is of the order of the inverse of the rate of change of the Hamiltonian; this yields

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Section: Quenching Through a Multicritical Pointmentioning

confidence: 99%

Section: And the New Hamiltonian Ismentioning

confidence: 99%

Section: A Spin Model: Transverse and Anisotropic Quenchingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Defect Production Due to Quenching Through a Multicritical Point and Along a Gapless Line

Divakaran

Mukherjee

Dutta

et al. 2010

Lecture Notes in Physics

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Non-equilibrium Dynamics of Quantum Systems: Order Parameter Evolution, Defect Generation, and Qubit Transfer

Mondal

Sen

Sengupta

2010

Quantum Quenching, Annealing and Computation

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The properties of systems near quantum critical points (QCPs) have been studied extensively in recent years [1,2]. A QCP is a point across which the symmetry of the ground state of a quantum system changes in a fundamental way; such a point can be accessed by changing some parameter, say λ , in the Hamiltonian governing the system. The change in the ground state across a QCP is mediated by quantum fluctuations. Unlike conventional thermal critical points, thermal fluctuations do not play a crucial role in such transitions. Similar to its thermal counterparts, the low energy physics near a QCP is associated with a number of critical exponents which characterize the universality class of such a transition. Amongst these exponents, the dynamical critical exponent z provides the signature of the relative scaling of space and time at the transition and has no counterpart in thermal phase transitions. The other exponent which is going to be important for the purpose of this review is the well-known correlation length exponent ν. These exponents are formally defined as follows. As we approach the critical point at λ = λ c , the correlation length diverges as ξ ∼ |λ − λ c | −ν , while the gap between the ground state and first excited state vanishes as ∆ E ∼ ξ −z ∼ |λ − λ c | zν . Exactly at the critical point λ = λ c , the energy of the low-lying excitations vanishes at some wave number k 0 as ω ∼ |k − k 0 | z . The critical exponents are independent of the details of the microscopic Hamiltonian; they depend only on a few parameters such as the dimensionality of the system and the symmetry of the order parameter. These features render the low energy equilibrium physics of a quantum system near a QCP truly universal.In contrast to this well-understood universality of the equilibrium properties of a system near a QCP, relatively few universal features are known in the nonequilibrium behavior of a quantum system. Initial studies in this field aimed at understanding the near-equilibrium finite temperature dynamics near a quantum critical

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Quench Dynamics of Quantum and Classical Ising Chains: From the Viewpoint of the Kibble–Zurek Mechanism

Suzuki

2010

Quantum Quenching, Annealing and Computation

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Quenching dynamics of a quantumXYspin-12chain in a transverse field

Cited by 157 publications

References 30 publications

Defect Production Due to Quenching Through a Multicritical Point and Along a Gapless Line

Defect Production Due to Quenching Through a Multicritical Point and Along a Gapless Line

Non-equilibrium Dynamics of Quantum Systems: Order Parameter Evolution, Defect Generation, and Qubit Transfer

Quench Dynamics of Quantum and Classical Ising Chains: From the Viewpoint of the Kibble–Zurek Mechanism

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