Kibble-Zurek scaling in periodically driven quantum systems

Russomanno, Angelo; Torre, Emanuele G. Dalla

doi:10.1209/0295-5075/115/30006

Cited by 31 publications

(47 citation statements)

References 101 publications

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“…[60]. The Floquet ground state is defined as the adiabatic continuation at finite frequency of the ground state of the high-frequency time-averaged Hamiltonian.…”

Section: The Spin Model and Its Fermionic Descriptionmentioning

confidence: 99%

“…The Floquet ground state is defined as the adiabatic continuation at finite frequency of the ground state of the high-frequency time-averaged Hamiltonian. In the high frequency limit, the ground state of the timeaveraged Hamiltonian is a legitimate Floquet state 26,60 . We can define the Floquet state which adiabatically continues it to lower frequencies with a prescription which goes as follows.…”

Section: The Spin Model and Its Fermionic Descriptionmentioning

confidence: 99%

“…It shares many properties with the ground state of the static systems. In particular, it has been shown that in integrable models, the entanglement entropy of the FGS generically follows an area law and is bounded in one dimension 60 . Furthermore, the FGS can undergo sharp phase transitions associated with degeneracies (resonances) of the Floquet spectrum.…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [60] we considered its FGS and showed that this is the specific state undergoing quantum phase transitions 81 . Here we significantly extend these results by deriving the full phase diagram of the model.…”

Section: Introductionmentioning

confidence: 99%

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Spin and topological order in a periodically driven spin chain

Russomanno¹,

Friedman²,

Torre³

2017

Phys. Rev. B

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The periodically driven quantum Ising chain has recently attracted a large attention in the context of Floquet engineering. In addition to the common paramagnet and ferromagnet, this driven model can give rise to new topological phases. In this work we systematically explore its quantum phase diagram, by examining the properties of its Floquet ground state. We specifically focus on driving protocols with time-reversal invariant points, and demonstrate the existence of an infinite number of distinct phases. These phases are separated by second-order quantum phase transitions, accompanied by continuous changes of local and string order parameters, as well as sudden changes of a topological winding number and of the number of protected edge states. When one of these phase transitions is adiabatically crossed, the correlator associated to the order parameter is nonvanishing over a length scale which shows a Kibble-Zurek scaling. In some phases, the Floquet ground state spontaneously breaks the discrete time-translation symmetry of the Hamiltonian. Our findings provide a better understanding of topological phases in periodically driven clean integrable models.

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“…[60]. The Floquet ground state is defined as the adiabatic continuation at finite frequency of the ground state of the high-frequency time-averaged Hamiltonian.…”

Section: The Spin Model and Its Fermionic Descriptionmentioning

confidence: 99%

Section: The Spin Model and Its Fermionic Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spin and topological order in a periodically driven spin chain

Russomanno¹,

Friedman²,

Torre³

2017

Phys. Rev. B

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“…Alternatively, toggling between Hamiltonians with solely Ising interactions or purely transverse fields yields an intrinsically dynamical FSPT phase which has no equilibrium analog. We explore the stability of both phases to long-range interactions and provide a detailed experimental blueprint using Rydberg-dressed atoms.ESPT phase-Inspired by pioneering work on emulating static phases in driven systems [22,32,33,[64][65][66][67][68], we first consider the realization of a many-body localized version of the Haldane phase [69]. This SPT phase can be protected by a discrete dihedral symmetry, Z 2 × Z 2 , and exhibits boundary modes that are odd under the symmetry; these edge modes behave as decoupled spin-1/2 degrees of freedom that are robust to any perturbation which preserves the symmetry.…”

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confidence: 99%

Floquet Symmetry-Protected Topological Phases in Cold-Atom Systems

et al. 2017

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We propose and analyze two distinct routes toward realizing interacting symmetry-protected topological (SPT) phases via periodic driving. First, we demonstrate that a driven transversefield Ising model can be used to engineer complex interactions which enable the emulation of an equilibrium SPT phase. This phase remains stable only within a parametric time scale controlled by the driving frequency, beyond which its topological features break down. To overcome this issue, we consider an alternate route based upon realizing an intrinsically Floquet SPT phase that does not have any equilibrium analog. In both cases, we show that disorder, leading to many-body localization, prevents runaway heating and enables the observation of coherent quantum dynamics at high energy densities. Furthermore, we clarify the distinction between the equilibrium and Floquet SPT phases by identifying a unique micromotion-based entanglement spectrum signature of the latter. Finally, we propose a unifying implementation in a one-dimensional chain of Rydbergdressed atoms and show that protected edge modes are observable on realistic experimental time scales.The discovery of topological insulators-materials which are insulating in their interior but can conduct on their surface-has led to a multitude of advances at the interface of condensed matter physics and materials engineering [1][2][3][4][5]. At their core, such insulators are characterized by the existence of nontrivial topology in their underlying single-particle electronic band structure [6, 7]. Generalizing our understanding of topological phases to the presence of strong many-body interactions represents one of the central questions in modern physics. Some of the simplest generalizations that have emerged along this direction are symmetry-protected topological (SPT) phases [8][9][10], which represent the minimal extension of topological band insulators to include many-body correlations. Featuring short-range entanglement, SPT phases do not exhibit anyonic excitations in their bulk, but nevertheless possess protected edge modes on their surface; as a result, they represent a particularly fertile ground for studying the interplay between symmetry, topology, and interactions.While indirect signatures of certain ground state SPTs have been observed in the solid state [11][12][13], directly probing the quantum coherence of their underlying edge modes represents an outstanding experimental challenge. In principle, cold-atom quantum simulations could offer a powerful additional tool set-including locally-resolved measurements and interferometric protocols-for probing the robustness of edge modes and systematically exploring their stability to specific perturbations [14][15][16][17][18]. Moreover, such platforms could also enable the controlled storage and transmission of quantum information [19][20][21]. Despite these advantages, and owing to the complexity of typical model SPT Hamiltonians, it remains difficult to engineer and stabilize SPT phases in coldatom systems. One approach to t...

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Open source Matrix Product States: Opening ways to simulate entangled many-body quantum systems in one dimension

Jaschke

Wall

Carr

2018

Computer Physics Communications

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Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States (MPSs), have attracted interest from different fields of quantum physics ranging from solid state systems to quantum simulators and quantum computing. Our open source MPS code provides the community with a toolset to analyze the statics and dynamics of one-dimensional quantum systems. Here, we present our open source library, Open Source Matrix Product States (OSMPS), of MPS methods implemented in Python and Fortran2003. The library includes tools for ground state calculation and excited states via the variational ansatz. We also support ground states for infinite systems with translational invariance. Dynamics are simulated with different algorithms, including three algorithms with support for long-range interactions. Convenient features include built-in support for fermionic systems and number conservation with rotational U(1) and discrete Z 2 symmetries for finite systems, as well as data parallelism with MPI. We explain the principles and techniques used in this library along with examples of how to efficiently use the general interfaces to analyze the Ising and Bose-Hubbard models. This description includes the preparation of simulations as well as dispatching and post-processing of them.Keywords: many-body quantum system; entangled quantum dynamics; Matrix Product State (MPS); quantum simulator; tensor network method; Density Matrix Renormalization Group (DMRG) PROGRAM SUMMARYProgram title: Open Source Matrix Product States (OSMPS), v2.0 Program summary and documentation: http://openmps.sourceforge.io/ Program obtainable from: http://sourceforge.net/p/openmps Licensing provisions: GNU GPL v3 (Minor parts follow the copyright of the Expokit package.) Programming language: Python, Fortran2003, MPI for parallel computing Compilers (Fortran): gfortran, ifort, g95Operating system: Linux, Mac OS X, Windows Supplementary material: We provide programs to reproduce selected figures in the Appendices. Nature of the problem: Solving the ground state and dynamics of a many-body entangled quantum system is a challenging problem; the Hilbert space grows exponentially with system size. Complete diagonalization of the Hilbert space to floating point precision is limited to less than forty qubits. Solution method: Matrix Product States in one spatial dimension overcome the exponentially growing Hilbert space by truncating the least important parts of it. The error can be well controlled. Local neighboring sites are variationally optimized in order to minimize the energy of the complete system. We can target the ground state and low lying excited states. Moreover, we offer various methods to solve the time evolution following the many-body Schrödinger equation. These methods include e.g. the Suzuki-Trotter decompositions using local propagators or the Krylov method, both approximating the pro...

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Kibble-Zurek scaling in periodically driven quantum systems

Cited by 31 publications

References 101 publications

Spin and topological order in a periodically driven spin chain

Spin and topological order in a periodically driven spin chain

Floquet Symmetry-Protected Topological Phases in Cold-Atom Systems

Open source Matrix Product States: Opening ways to simulate entangled many-body quantum systems in one dimension

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