Quantum phase transitions detected by a local probe using time correlations and violations of Leggett-Garg inequalities

Gómez-Ruiz, Fernando Javier; Mendoza‐Arenas, J. J.; Rodríguez, F. J.; Tejedor, C.; Quiroga, Luis

doi:10.1103/physrevb.93.035441

Cited by 17 publications

(21 citation statements)

References 62 publications

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“…In light of recent experiments [24], we also demonstrate that certain dynamical "qubit" correlation functions exhibit phase-sensitive signatures even in the presence of disorder [26][27][28]. Specifically, we find that the appearance of (non)-local zero-modes will manifest themselves in the long-time behavior of (non)-local correlators.…”

supporting

confidence: 68%

Disorder protected and induced local zero-modes in longer-range Kitaev chains

2018

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We study the effects of disorder on a Kitaev chain with longer-range hopping and pairing terms which is capable of forming local zero energy excitations and, hence, serves as a minimal model for localization-protected edge qubits. The clean phase diagram hosts regions with 0, 1, and 2 Majorana zero-modes (MZMs) per edge. Using a semi-analytic approach corroborated by numerical calculations of the entanglement degeneracy, we show how phase boundaries evolve under the influence of disorder. While in general the 2 MZM region is stable with respect to moderate disorder, stronger values drive transition towards the topologically trivial phase. We uncover regions where the addition of disorder induces local zero-modes absent for the corresponding clean system. Interestingly, we discover that disorder destroys any direct transition between phases with zero and two MZMs by creating a tricritical point at the 2-0 MZM boundary of the clean system. Finally, motivated by recent experiments, we calculate the characteristic signatures of the disorder phase diagram as measured in dynamical local and non-local "qubit" correlation functions. Our work provides a minimal starting point to investigate the coherence properties of local qubits in the presence of disorder.The Kitaev superconductor p-wave chain [1] supports an inherently non-local ground state degeneracy, making it possible to create a qubit which is highly fault-tolerant to local decoherence processes [2] interesting for quantum information technology [3]. While the non-locality of the zero-mode offers this protection, it also poses an experimental challenge since non-local measurements are generally difficult [4,5]. Local qubits formed at the edge of topological chains can exhibit remarkable coherence properties when the bulk system is in a many-body localized state [6,7]. Intuitively, this can be understood from the localization of bulk excitations, which once excited thermally for example, typically decohere the qubit state. However, their detrimental effects may be suppressed in disordered systems due to lack of thermalization [6,8]. This potentially provides a route to achieve both stable qubits and better experimental controllability.Motivated by these ideas, we study the effects of disorder on the topological phase diagram for a minimal variant of the Kitaev chain which enables both local and nonlocal qubit formation [9]. (This system can also be viewed as a three-spin 'cluster' transverse-field Ising model via Jordan-Wigner transformation [10].) The Z classification [11] of the model allows two Majorana zero-modes (MZMs) to form on each side of the chain which can pair up to form a local zero-energy excitation [12]. Previous works have investigated the role of disorder in topological chains with MZMs [13-20] and found that the clean phase diagram is generally robust for weak values of disorder but strong disorder drives the system into a topologically trivial phase. While the issue is of central importance in conventional solid-state setups [21][22][23], recent...

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supporting

confidence: 68%

Disorder protected and induced local zero-modes in longer-range Kitaev chains

2018

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“…As a result, the direction and magnitude of the overall maximal violation can be controlled by ∆, being enhanced in the strongly-interacting regime. This also shows that the LGI violation indicates the nonequilibrium critical point, a property that it also features in equilibrium [57,58].…”

Section: We Show the Maximal Violations K αmentioning

confidence: 55%

Enhancing violations of Leggett-Garg inequalities in nonequilibrium correlated many-body systems by interactions and decoherence

Mendoza‐Arenas

Gómez-Ruiz

Rodríguez

et al. 2019

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We identify different schemes to enhance the violation of Leggett-Garg inequalities in open many-body systems. Considering a nonequilibrium archetypical setup of quantum transport, we show that particle interactions control the direction and amplitude of maximal violation, and that in the strongly-interacting and strongly-driven regime bulk dephasing enhances the violation. Through an analytical study of a minimal model we unravel the basic ingredients to explain this decoherence-enhanced quantumness, illustrating that such an effect emerges in a wide variety of systems.

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“…Note that these results are strictly valid for an infinitely long chain or for times below a certain limit where finite size effects could emerge, such as possible interference or revivals coming from the reflected influence of the other edge (not shown here). In addition, the quantum behavior of single-site TTC for the edge single-and double-Majorana qubits is similar to the x and z spin correlations of the transverse Ising model, and consequently its quantum critical point could also be detected by TTC measurements [37].…”

Section: Resultsmentioning

confidence: 77%

“…The key quantity of interest in the present work is the symmetrized TTC, C (t 1 , t 2 ), as given by the expression [37] C (t 1 ,…”

Section: B Two-time Correlationsmentioning

confidence: 99%

Universal two-time correlations, out-of-time-ordered correlators, and Leggett-Garg inequality violation by edge Majorana fermion qubits

et al. 2018

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In the present work we propose that two-time correlations of Majorana edge localized fermions constitute a novel and versatile toolbox for assessing the topological phases of 1D open lattices. Using analytical and numerical calculations on the Kitaev model, we uncover universal relationships between the decay of the short-time correlations and a particular family of out-of-time-ordered correlators, which provide direct experimental alternatives to the quantitative analysis of the system regime, either normal or topological. Furthermore we show that the saturation of two-time correlations possesses features of an order parameter. Finally, we find that violations of Leggett-Garg inequalities can indicate the topological-normal phase transition by looking at different qubits formed by pairing local and non-local edge Majorana fermions.

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Quantum phase transitions detected by a local probe using time correlations and violations of Leggett-Garg inequalities

Cited by 17 publications

References 62 publications

Disorder protected and induced local zero-modes in longer-range Kitaev chains

Disorder protected and induced local zero-modes in longer-range Kitaev chains

Enhancing violations of Leggett-Garg inequalities in nonequilibrium correlated many-body systems by interactions and decoherence

Universal two-time correlations, out-of-time-ordered correlators, and Leggett-Garg inequality violation by edge Majorana fermion qubits

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