Probing Majorana modes via local spin dynamics
Research output: Contribution to journal › Journal article › Research › peer-review
Standard
Probing Majorana modes via local spin dynamics. / Bjerlin, Johannes; Sorensen, Anders S.; Haas, Stephan.
In: Physical Review B, Vol. 106, No. 3, 035414, 14.07.2022.Research output: Contribution to journal › Journal article › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Probing Majorana modes via local spin dynamics
AU - Bjerlin, Johannes
AU - Sorensen, Anders S.
AU - Haas, Stephan
PY - 2022/7/14
Y1 - 2022/7/14
N2 - We investigate Majorana modes in a quantum spin chain with bond-dependent exchange interactions by studying its dynamics. Specifically, we consider two-time correlations for the anisotropic Kitaev-Heisenberg (KH) Hamiltonian close to the so-called Kitaev critical point. Here the model coincides with a phase boundary of two uncoupled instances of Kitaev???s model for p-wave superconductors, together supporting a degenerate ground state characterized by multiple Majorana modes. In this regime, the real-time dynamics of local spins reveal a set of strong zero modes, corresponding to a set of protruding frequencies in the two-time correlation function. We derive perturbative interactions that map the KH spin chain onto the topological regime of Kitaev???s fermionic model, thus opening up a bulk gap while retaining almost degenerate modes in the mesoscopic regime, i.e., for finite system sizes. This showcases the emergence of Majorana modes in a chain of effective dimers. Here, the binding energy within each unit cell competes with the interdimer coupling to generate a finite-size energy gap, in analogy with local energy terms in the transverse-field Ising model. These modes give rise to long coherence times of local spins located at the system edges. By breaking the local symmetry in each dimer, one can also observe a second class of Majorana modes in terms of a beating frequency in the two-time correlations function of the edge spin. Furthermore, we develop a scenario for realizing these model predictions in ion-trap quantum simulators with collective addressing of the ions.
AB - We investigate Majorana modes in a quantum spin chain with bond-dependent exchange interactions by studying its dynamics. Specifically, we consider two-time correlations for the anisotropic Kitaev-Heisenberg (KH) Hamiltonian close to the so-called Kitaev critical point. Here the model coincides with a phase boundary of two uncoupled instances of Kitaev???s model for p-wave superconductors, together supporting a degenerate ground state characterized by multiple Majorana modes. In this regime, the real-time dynamics of local spins reveal a set of strong zero modes, corresponding to a set of protruding frequencies in the two-time correlation function. We derive perturbative interactions that map the KH spin chain onto the topological regime of Kitaev???s fermionic model, thus opening up a bulk gap while retaining almost degenerate modes in the mesoscopic regime, i.e., for finite system sizes. This showcases the emergence of Majorana modes in a chain of effective dimers. Here, the binding energy within each unit cell competes with the interdimer coupling to generate a finite-size energy gap, in analogy with local energy terms in the transverse-field Ising model. These modes give rise to long coherence times of local spins located at the system edges. By breaking the local symmetry in each dimer, one can also observe a second class of Majorana modes in terms of a beating frequency in the two-time correlations function of the edge spin. Furthermore, we develop a scenario for realizing these model predictions in ion-trap quantum simulators with collective addressing of the ions.
KW - QUANTUM PHASE-TRANSITION
KW - ENTANGLEMENT
KW - ANYONS
KW - STATES
KW - IONS
U2 - 10.1103/PhysRevB.106.035414
DO - 10.1103/PhysRevB.106.035414
M3 - Journal article
VL - 106
JO - Physical Review B
JF - Physical Review B
SN - 2469-9950
IS - 3
M1 - 035414
ER -
ID: 315759742