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6CCVD Research

Floquet dynamical quantum phase transitions in periodically quenched systems

At a Glance

Section titled “At a Glance”
MetadataDetails
Publication Date2021-06-15
JournalJournal of Physics Condensed Matter
AuthorsLongwen Zhou, Qianqian Du, Longwen Zhou, Qianqian Du
InstitutionsOcean University of China
Citations24
AnalysisFull AI Review Included

Executive Summary

Section titled “Executive Summary”
  • Floquet Engineering of DQPTs: A theoretical framework was developed to utilize periodic quenching (Floquet engineering) to precisely control and induce multiple Dynamical Quantum Phase Transitions (DQPTs) within a single driving period.
  • Multiple Transitions: By increasing the amplitude of the quench parameters (Jx, Jy), the system exhibits a corresponding increase in the number of DQPTs, manifesting as nonanalytic cusps in the return rate function f(t).
  • Topological Characterization: The transitions are characterized by a Dynamical Topological Order Parameter (DTOP), wv(t), derived from the noncyclic geometric phase of the evolving Floquet states.
  • Quantized Jumps: The DTOP exhibits robust, quantized integer jumps (Δwv ∈ Z) at every critical time (tc) of a Floquet DQPT, serving as a dynamical topological invariant.
  • Phase Discrimination: The behavior of the DTOP successfully discriminates between different underlying Floquet topological phases (gapped vs. gapless), offering a dynamical tool for phase boundary detection.
  • Experimental Realizability: The model (Piecewise Quenched Lattice, PQL) is directly realizable in existing quantum simulator platforms, notably Nitrogen-Vacancy (NV) centers in diamonds and 87Rb Bose-Einstein Condensates (BECs).

Technical Specifications

Section titled “Technical Specifications”
ParameterValueUnitContext
Driving Period (T)2DimensionlessSet for theoretical modeling (T=2).
Planck Constant (ħ)1DimensionlessSet for theoretical modeling.
Quench Amplitudes (Jx, Jy)Up to 4.1πDimensionlessControl parameters for inducing multiple DQPTs.
Critical Time (tc)sc + 2lDimensionlessTime of DQPT occurrence, where sc is the micromotion time (sc ∈ [0, 2)).
DTOP Jump Magnitude (Δwv)Integer (1, 2, etc.)QuantizedChange in the Dynamical Topological Order Parameter at tc.
Numerical Integration Grid (N)300GridsNumber of k-space points used to simulate the thermodynamic limit (N → ∞).
Experimental Jx, Jy RangeUp to 3DimensionlessAchievable coupling strengths in recent NV center experiments (Ref. [61]).
Observation Time Window6”sTypical duration over which DQPT features remain clearly observable in NV center setups (3 driving periods).

Key Methodologies

Section titled “Key Methodologies”
  1. Hamiltonian Definition: Employed a general time-periodic, piecewise quenched Hamiltonian H(k,t) possessing chiral (sublattice) symmetry, alternating between Hx(k)σx and Hy(k)σy over the period T=2.
  2. Model Specification: The general framework was applied to the Piecewise Quenched Lattice (PQL) model, defined by quench functions hx(k) = Jx cos k and hy(k) = Jy sin k.
  3. Floquet State Initialization: The system was initialized in a uniformly filled Floquet band, corresponding to a specific Floquet eigenstate |ψv(k)>.
  4. DQPT Detection via Rate Function: The rate function of return probability, f(t), was calculated by integrating the return probability gv(k,t) over the first Brillouin zone. DQPTs were identified by the nonanalytic cusps in f(t).
  5. Analytical Critical Conditions: Analytical expressions were derived (Eqs. 40-43) for the critical momenta (kc) and critical times (tc) based on the vanishing of the return amplitude Gv(k,s).
  6. DTOP Calculation: The Dynamical Topological Order Parameter (DTOP), wv(t), was computed as the winding number of the noncyclic geometric phase, φGv(k,t), integrated over k-space.

Commercial Applications

Section titled “Commercial Applications”
  • Quantum Simulation Platforms: Provides validated theoretical protocols for simulating complex non-equilibrium dynamics using solid-state quantum simulators, particularly the NV center in diamond setup.
  • Topological Quantum Computing: DTOPs offer a robust, quantized metric for dynamically detecting and characterizing topological phase transitions, essential for verifying the stability of topological qubits.
  • Floquet Protocol Engineering: The ability to control the number and timing of DQPTs within a finite time window allows for the flexible design of novel quantum protocols and dynamical gates.
  • Quantum Metrology and Sensing: Utilizing the NV center platform, the framework enables the dynamical detection of topological phases, potentially enhancing the capabilities of solid-state quantum sensors.
  • Non-Equilibrium Materials Science: Advances the classification and characterization of novel non-equilibrium phases of matter, such as Floquet topological insulators and time crystals.
View Original Abstract

Abstract Dynamical quantum phase transitions (DQPTs) are characterized by nonanalytic behaviors of physical observables as functions of time. When a system is subject to time-periodic modulations, the nonanalytic signatures of its observables could recur periodically in time, leading to the phenomena of Floquet DQPTs. In this work, we systematically explore Floquet DQPTs in a class of periodically quenched one-dimensional system with chiral symmetry. By tuning the strength of quench, we find multiple Floquet DQPTs within a single driving period, with more DQPTs being observed when the system is initialized in Floquet states with larger topological invariants. Each Floquet DQPT is further accompanied by the quantized jump of a dynamical topological order parameter, whose values remain quantized in time if the underlying Floquet system is prepared in a gapped topological phase. The theory is demonstrated in a piecewise quenched lattice model, which possesses rich Floquet topological phases and is readily realizable in quantum simulators like the nitrogen-vacancy center in diamonds. Our discoveries thus open a new perspective for the Floquet engineering of DQPTs and the dynamical detection of topological phase transitions in Floquet systems.

Tech Support

Section titled “Tech Support”

Original Source

Section titled “Original Source”

References

Section titled “References”
  1. 2013 - Dynamical quantum phase transitions in the transverse-field Ising model [Crossref]
  2. 2010 - Dynamics after a sweep through a quantum critical point [Crossref]
  3. 2018 - Dynamical quantum phase transitions in non-Hermitian lattices [Crossref]
  4. 2014 - Dynamical quantum phase transitions in systems with broken-symmetry phases [Crossref]
  5. 2014 - First-order dynamical phase transitions [Crossref]
  6. 2014 - Disentangling dynamical phase transitions from equilibrium phase transitions [Crossref]
  7. 2015 - Scaling and universality at dynamical quantum phase transitions [Crossref]
  8. 2016 - Dynamical quantum phase transitions: role of topological nodes in wave function overlaps [Crossref]
  9. 2017 - Quenching a quantum critical state by the order parameter: dynamical quantum phase transitions and quantum speed limits [Crossref]
  10. 2019 - Quench dynamics and zero-energy modes: the case of the Creutz model [Crossref]

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