Tuning the presence of dynamical phase transitions in a generalized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math>spin chain

Divakaran, Uma; Sharma, Shraddha; Dutta, Amit

doi:10.1103/physreve.93.052133

Cited by 53 publications

(42 citation statements)

References 79 publications

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“…and that the leading eigenvalue of τ s N (0) lies in the S z = 0 sector. In order to get an intuition of the corresponding Y -functions y (69), (70). Note that a crucial ingredient for this is the knowledge of the functions Φ The above analytical structure has been verified numerically up to N = 8.…”

Section: The Non-linear Integral Equations For the Delta-statementioning

confidence: 82%

Integrable quenches in nested spin chains II: fusion of boundary transfer matrices

Piroli¹,

Vernier²,

Calabrese³

et al. 2019

J. Stat. Mech.

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We consider quantum quenches in the integrable SU (3)-invariant spin chain (Lai-Sutherland model), and focus on the family of integrable initial states. By means of a Quantum Transfer Matrix approach, these can be related to "soliton-non-preserving" boundary transfer matrices in an appropriate transverse direction. In this work, we provide a technical analysis of such integrable transfer matrices. In particular, we address the computation of their spectrum: this is achieved by deriving a set of functional relations between the eigenvalues of certain "fused operators" that are constructed starting from the soliton-non-preserving boundary transfer matrices (namely the T -and Y -systems). As a direct physical application of our analysis, we compute the Loschmidt echo for imaginary and real times after a quench from the integrable states. Our results are also relevant for the study of the spectrum of SU (3)-invariant Hamiltonians with open boundary conditions.

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Section: The Non-linear Integral Equations For the Delta-statementioning

confidence: 82%

Integrable quenches in nested spin chains II: fusion of boundary transfer matrices

Piroli¹,

Vernier²,

Calabrese³

et al. 2019

J. Stat. Mech.

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“…[32] and the lines of FZs were indeed found to cross the real time axis at those instants. This observation has been independently confirmed through several works on quenched one-dimensional (1D) integrable and non-integrable systems [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. Subsequent studies, however, have established that sudden quenching within the same phase of a system (both integrable and non-integrable) without ever encountering an equilibrium QCP may still give rise to DQPTs in some situations [54,55].…”

Section: Introductionmentioning

confidence: 84%

Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model

Bhattacharya

Dutta

2017

Phys. Rev. B

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We study the behavior of Fisher Zeros (FZs) and dynamical quantum phase transitions (DQPTs) for a linearly ramped Haldane model occurring in the subsequent temporal evolution of the same and probe the intimate connection with the equilibrium topology of the model. Here, we investigate the temporal evolution of the final state of the Haldane Hamiltonian (evolving with time-independent final Hamiltonian) reached following a linear ramping of the staggered (Semenoff) mass term from an initial to a final value, first selecting a specific protocol, so chosen that the system is ramped from one non-topological phase to the other through a topological phase. We establish the existence of three possible behaviour of areas of FZs corresponding to a given sector: (i) no-DQPT, (ii) one-DQPT (intermediate) and (iii)two-DQPTs (re-entrant), depending on the inverse quenching rate τ . Our study also reveals that the appearance of the areas of FZs is an artefact of the nonzero (quasi-momentum dependent) Haldane mass (MH ), whose absence leads to an emergent onedimensional behaviour indicated by the shrinking of the areas FZs to lines and the non-analyticity in the dynamical "free energy" itself. Moreover, the characteristic rates of crossover between the three behaviour of FZs are determined by the time-reversal invariant quasi-momentum points of the Brillouin zone where MH vanishes. Thus, we observe that through the presence or absence of MH , there exists an intimate relation to the topological properties of the equilibrium model even when the ramp drives the system far away from equilibrium.

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“…Further studies, however, revealed that DQPTs can occur following a quench also within the same phase [48][49][50]. Other theoretical works have explored DQPTs in topological and mixed phases [72][73][74][75][76] and also after slow quenches ("ramps") [77][78][79].…”

Section: Dynamical Quantum Phase Transitionsmentioning

confidence: 99%

Quench dynamics and zero-energy modes: The case of the Creutz model

et al. 2019

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In most lattice models, the closing of a band gap typically occurs at high-symmetry points in the Brillouin zone. Differently, in the Creutz model − describing a system of spinless fermions hopping on a two-leg ladder pierced by a magnetic field − the gap closing at the quantum phase transition between the two topologically nontrivial phases of the model can be moved by tuning the hopping amplitudes. We take advantage of this property to examine the nonequilibrium dynamics of the model after a sudden quench of the magnetic flux through the plaquettes of the ladder. For a quench to one of the equilibrium quantum critical points we find that the revival period of the Loschmidt echo − measuring the overlap between initial and time-evolved states − is controlled by the gap closing zero-energy modes. In particular, and contrary to expectations, the revival period of the Loschmidt echo for a finite ladder does not scale linearly with size but exhibits jumps determined by the presence or absence of zero-energy modes. We further investigate the conditions for the appearance of dynamical quantum phase transitions in the model and find that, for a quench to an equilibrium critical point, such transitions occur only for ladders of sizes which host zero-energy modes. Exploiting concepts from quantum thermodynamics, we show that the average work and the irreversible work per lattice site exhibit a weak dependence on the size of the system after a quench across an equilibrium critical point, suggesting that quenching into a different phase induces effective correlations among the particles.

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Tuning the presence of dynamical phase transitions in a generalizedXYspin chain

Cited by 53 publications

References 79 publications

Integrable quenches in nested spin chains II: fusion of boundary transfer matrices

Integrable quenches in nested spin chains II: fusion of boundary transfer matrices

Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model

Quench dynamics and zero-energy modes: The case of the Creutz model

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