Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1601.05476 · Physical review. E

Edge mode dynamics of quenched topological wires

Pedro D Sacramento

Published Jun 13, 2016• 24 citations
arXivHTMLPDF

Abstract

The fermionic and Majorana edge mode dynamics of various topological systems are compared, after a sudden global quench of the Hamiltonian parameters takes place. Attention is focused on the regimes where the survival probability of an edge state has oscillations either due to critical or off-critical quenches. The nature of the wave functions and the overlaps between the eigenstates of different points in parameter space determine the various types of behaviors, and the distinction due to the Majorana nature of the excitations plays a lesser role. Performing a sequence of quenches, it is shown that the edge states, including Majorana modes, may be switched off and on. Also, the generation of Majoranas due to quenching from a trivial phase is discussed.

DOI
10.1103/physreve.93.062117

Related papers

Dynamics of Quenched Topological Edge Modes

Pedro D Sacramento

A characteristic feature of topological systems is the presence of robust gapless edge states. In this work the effect of time-dependent perturbations on the edge states is considered. Specifically we consider perturbations that can be understood as changes of the parameters of the Hamiltonian. These changes may be sudden or carried out at a fixed rate. In general, the edge modes decay in the thermodynamic limit, but for finite systems a revival time is found that scales with the system size. The dynamics of fermionic edge modes and Majorana modes are compared. The effect of periodic perturbations is also referred allowing the appearance of edge modes out of a topologically trivial phase.

arXiv:1701.03567•Nov 26, 2017•1 citation

Survival probability of an edge Majorana in a one-dimensional p -wave superconducting chain under sudden quenching of parameters

Atanu Rajak, Amit Dutta

We consider the temporal evolution of a zero-energy edge Majorana of a spinless p-wave superconducting chain following a sudden change of a parameter of the Hamiltonian. Starting from one of the topological phases that has an edge Majorana, the system is suddenly driven to the other topological phase or to the (topologically) trivial phases and to the quantum critical points (QCPs) separating these phases. The survival probability of the initial edge Majorana as a function of time is studied following the quench. Interestingly when the chain is quenched to the QCP, we find a nearly perfect oscillation of the survival probability, indicating that the Majorana travels back and forth between two ends, with a time period that scales with the system size. We also generalize to the situation when there is a next-nearest-neighbor hopping in a superconducting chain and there results in a pair of edge Majorana at each end of the chain in the topological phase. We show that the frequency of oscillation of the survival probability gets doubled in this case. We also perform an instantaneous quenching of the Hamiltonian (with two Majorana modes at each end of the chain) to an another Hamiltonian which has only one Majorana mode in equilibrium; the MSP shows oscillations as a function of time with a noticeable decay in the amplitude. On the other hand for a quenching which is reverse to the previous one, the MSP decays rapidly and stays close to zero with fluctuations in amplitude.

arXiv:1312.7109•Physical Review E•Apr 15, 2014•52 citations

Quench dynamics and parity blocking in Majorana wires

Suraj Hegde, Vasudha Shivamoggi, Smitha Vishveshwara +1 more

We theoretically explore quench dynamics in a finite-sized topological fermionic p -wave superconducting wire with the goal of demonstrating that topological order can have marked effects on such non-equilibrium dynamics. In the case studied here, topological order is reflected in the presence of two (nearly) isolated Majorana fermionic end bound modes together forming an electronic state that can be occupied or not, leading to two (nearly) degenerate ground states characterized by fermion parity. Our study begins with a characterization of the static properties of the finite-sized wire, including the behavior of the Majorana end modes and the form of the tunnel coupling between them; a transfer matrix approach to analytically determine the locations of the zero energy contours where this coupling vanishes; and a Pfaffian approach to map the ground state parity in the associated phase diagram. We next study the quench dynamics resulting from initializing the system in a topological ground state and then dynamically tuning one of the parameters of the Hamiltonian. For this, we develop a dynamic quantum many-body technique that invokes a Wick's theorem for Majorana fermions, vastly reducing the numerical effort given the exponentially large Hilbert space. We investigate the salient and detailed features of two dynamic quantities—the overlap between the time-evolved state and the instantaneous ground state (adiabatic fidelity) and the residual energy. When the parity of the instantaneous ground state flips successively with time, we find that the time-evolved state can dramatically switch back and forth between this state and an excited state even when the quenching is very slow, a phenomenon that we term 'parity blocking'. This parity blocking becomes prominently manifest as non-analytic jumps as a function of time in both dynamic quantities.

arXiv:1412.5255•New Journal of Physics•May 22, 2015•52 citations

Quench dynamics and parity blocking in Majorana wires

Suraj Hegde, Vasudha Shivamoggi, Smitha Vishveshwara +1 more

We theoretically explore quench dynamics in a finite-sized topological fermionic p-wave superconducting wire with the goal of demonstrating that topological order can have marked effects on such non-equilibrium dynamics. In the case studied here, topological order is reflected in the presence of two (nearly) isolated Majorana fermionic end bound modes together forming an electronic state that can be occupied or not, leading to two (nearly) degenerate ground states characterized by fermion parity. Our study begins with a characterization of the static properties of the finite-sized wire, including the behavior of the Majorana end modes and the form of the tunnel coupling between them; a transfer matrix approach to analytically determine the locations of the zero energy contours where this coupling vanishes; and a Pfaffian approach to map the ground state parity in the associated phase diagram. We next study the quench dynamics resulting from initializing the system in a topological ground state and then dynamically tuning one of the parameters of the Hamiltonian. For this, we develop a dynamic quantum many-body technique that invokes a Wick's theorem for Majorana fermions, vastly reducing the numerical effort given the exponentially large Hilbert space. We investigate the salient and detailed features of two dynamic quantities-the overlap between the time-evolved state and the instantaneous ground state (adiabatic fidelity) and the residual energy. When the parity of the instantaneous ground state flips successively with time, we find that the time-evolved state can dramatically switch back and forth between this state and an excited state even when the quenching is very slow, a phenomenon that we term `parity blocking'. This parity blocking becomes prominently manifest as non-analytic jumps as a function of time in both dynamic quantities.

•Jan 1, 2015•43 citations

Fate of Majorana fermions and Chern numbers after a quantum quench

Pedro D Sacramento

In the sequence of quenches to either nontopological phases or other topological phases, we study the stability of Majorana fermions at the edges of a two-dimensional topological superconductor with spin-orbit coupling and in the presence of a Zeeman term. Both instantaneous and slow quenches are considered. In the case of instantaneous quenches, the Majorana modes generally decay, but for a finite system there is a revival time that scales to infinity as the system size grows. Exceptions to this decaying behavior are found in some cases due to the presence of edge states with the same momentum in the final state. Quenches to a topological Z(2) phase reveal some robustness of the Majorana fermions in the sense that even though the survival probability of the Majorana state is small, it does not vanish. If the pairing is not aligned with the spin-orbit Rashba coupling, it is found that the Majorana fermions are fairly robust with a finite survival probability. It is also shown that the Chern number remains invariant after the quench, until the propagation of the mode along the transverse direction reaches the middle point, beyond which the Chern number fluctuates between increasing values. The effect of varying the rate of change in slow quenches is also analyzed. It is found that the defect production is nonuniversal and does not follow the Kibble-Zurek scaling with the quench rate, as obtained before for other systems with topological edge states.

arXiv:1404.5141•Physical Review E•Sep 29, 2014•66 citations

Pulse dynamics of quantum systems with pairing

Andrei A. Zvyagin

The evolution of the system of fermions with pairing under the action of a pulse (or a quench) of the external potential has been studied. In the dynamical regime the number of fermions oscillates (with beats) as a function of the duration of the pulse (or as a function of time for the quench) about the value determined by the magnitude of the pulse. Oscillations depend on the values of the potential and the pulse. The parameters of those oscillations permit one to determine characteristics of the dynamical quantum phase transitions, such as Fisher's zeros in one-dimensional systems. The effect is absent for zero pairing. In particular, the response of a topological superconductor to the pulse manifests dynamical oscillations, most pronounced for the range of parameters in which the topological superconductivity can occur. The response of Majorana edge states to the pulse is analyzed. The results are generalized for the bosonic system with pairing under the action of the pulse (quench).

Physical Review B•Nov 11, 2015•14 citations
The fermionic and Majorana edge mode dynamics of various topological systems are compared, after a sudden global quench of the Hamiltonian parameters takes place. Attention is focused on the regimes where the survival probability of an edge state has oscillations either due to critical or off-critical quenches. The nature of the wave functions and the overlaps between the eigenstates of different points in parameter space determine the various types of behaviors, and the distinction due to the Majorana nature of the excitations plays a lesser role. Performing a sequence of quenches, it is shown that the edge states, including Majorana modes, may be switched off and on. Also, the generation of Majoranas due to quenching from a trivial phase is discussed.
A characteristic feature of topological systems is the presence of robust gapless edge states. In this work the effect of time-dependent perturbations on the edge states is considered. Specifically we consider perturbations that can be understood as changes of the parameters of the Hamiltonian. These changes may be sudden or carried out at a fixed rate. In general, the edge modes decay in the thermodynamic limit, but for finite systems a revival time is found that scales with the system size. The dynamics of fermionic edge modes and Majorana modes are compared. The effect of periodic perturbations is also referred allowing the appearance of edge modes out of a topologically trivial phase.
We consider the temporal evolution of a zero-energy edge Majorana of a spinless p-wave superconducting chain following a sudden change of a parameter of the Hamiltonian. Starting from one of the topological phases that has an edge Majorana, the system is suddenly driven to the other topological phase or to the (topologically) trivial phases and to the quantum critical points (QCPs) separating these phases. The survival probability of the initial edge Majorana as a function of time is studied following the quench. Interestingly when the chain is quenched to the QCP, we find a nearly perfect oscillation of the survival probability, indicating that the Majorana travels back and forth between two ends, with a time period that scales with the system size. We also generalize to the situation when there is a next-nearest-neighbor hopping in a superconducting chain and there results in a pair of edge Majorana at each end of the chain in the topological phase. We show that the frequency of oscillation of the survival probability gets doubled in this case. We also perform an instantaneous quenching of the Hamiltonian (with two Majorana modes at each end of the chain) to an another Hamiltonian which has only one Majorana mode in equilibrium; the MSP shows oscillations as a function of time with a noticeable decay in the amplitude. On the other hand for a quenching which is reverse to the previous one, the MSP decays rapidly and stays close to zero with fluctuations in amplitude.
We theoretically explore quench dynamics in a finite-sized topological fermionic p -wave superconducting wire with the goal of demonstrating that topological order can have marked effects on such non-equilibrium dynamics. In the case studied here, topological order is reflected in the presence of two (nearly) isolated Majorana fermionic end bound modes together forming an electronic state that can be occupied or not, leading to two (nearly) degenerate ground states characterized by fermion parity. Our study begins with a characterization of the static properties of the finite-sized wire, including the behavior of the Majorana end modes and the form of the tunnel coupling between them; a transfer matrix approach to analytically determine the locations of the zero energy contours where this coupling vanishes; and a Pfaffian approach to map the ground state parity in the associated phase diagram. We next study the quench dynamics resulting from initializing the system in a topological ground state and then dynamically tuning one of the parameters of the Hamiltonian. For this, we develop a dynamic quantum many-body technique that invokes a Wick's theorem for Majorana fermions, vastly reducing the numerical effort given the exponentially large Hilbert space. We investigate the salient and detailed features of two dynamic quantities—the overlap between the time-evolved state and the instantaneous ground state (adiabatic fidelity) and the residual energy. When the parity of the instantaneous ground state flips successively with time, we find that the time-evolved state can dramatically switch back and forth between this state and an excited state even when the quenching is very slow, a phenomenon that we term 'parity blocking'. This parity blocking becomes prominently manifest as non-analytic jumps as a function of time in both dynamic quantities.
We theoretically explore quench dynamics in a finite-sized topological fermionic p-wave superconducting wire with the goal of demonstrating that topological order can have marked effects on such non-equilibrium dynamics. In the case studied here, topological order is reflected in the presence of two (nearly) isolated Majorana fermionic end bound modes together forming an electronic state that can be occupied or not, leading to two (nearly) degenerate ground states characterized by fermion parity. Our study begins with a characterization of the static properties of the finite-sized wire, including the behavior of the Majorana end modes and the form of the tunnel coupling between them; a transfer matrix approach to analytically determine the locations of the zero energy contours where this coupling vanishes; and a Pfaffian approach to map the ground state parity in the associated phase diagram. We next study the quench dynamics resulting from initializing the system in a topological ground state and then dynamically tuning one of the parameters of the Hamiltonian. For this, we develop a dynamic quantum many-body technique that invokes a Wick's theorem for Majorana fermions, vastly reducing the numerical effort given the exponentially large Hilbert space. We investigate the salient and detailed features of two dynamic quantities-the overlap between the time-evolved state and the instantaneous ground state (adiabatic fidelity) and the residual energy. When the parity of the instantaneous ground state flips successively with time, we find that the time-evolved state can dramatically switch back and forth between this state and an excited state even when the quenching is very slow, a phenomenon that we term `parity blocking'. This parity blocking becomes prominently manifest as non-analytic jumps as a function of time in both dynamic quantities.
In the sequence of quenches to either nontopological phases or other topological phases, we study the stability of Majorana fermions at the edges of a two-dimensional topological superconductor with spin-orbit coupling and in the presence of a Zeeman term. Both instantaneous and slow quenches are considered. In the case of instantaneous quenches, the Majorana modes generally decay, but for a finite system there is a revival time that scales to infinity as the system size grows. Exceptions to this decaying behavior are found in some cases due to the presence of edge states with the same momentum in the final state. Quenches to a topological Z(2) phase reveal some robustness of the Majorana fermions in the sense that even though the survival probability of the Majorana state is small, it does not vanish. If the pairing is not aligned with the spin-orbit Rashba coupling, it is found that the Majorana fermions are fairly robust with a finite survival probability. It is also shown that the Chern number remains invariant after the quench, until the propagation of the mode along the transverse direction reaches the middle point, beyond which the Chern number fluctuates between increasing values. The effect of varying the rate of change in slow quenches is also analyzed. It is found that the defect production is nonuniversal and does not follow the Kibble-Zurek scaling with the quench rate, as obtained before for other systems with topological edge states.
The evolution of the system of fermions with pairing under the action of a pulse (or a quench) of the external potential has been studied. In the dynamical regime the number of fermions oscillates (with beats) as a function of the duration of the pulse (or as a function of time for the quench) about the value determined by the magnitude of the pulse. Oscillations depend on the values of the potential and the pulse. The parameters of those oscillations permit one to determine characteristics of the dynamical quantum phase transitions, such as Fisher's zeros in one-dimensional systems. The effect is absent for zero pairing. In particular, the response of a topological superconductor to the pulse manifests dynamical oscillations, most pronounced for the range of parameters in which the topological superconductivity can occur. The response of Majorana edge states to the pulse is analyzed. The results are generalized for the bosonic system with pairing under the action of the pulse (quench).