Topology and $\mathcal{PT}$ Symmetry in a Non-Hermitian Su-Schrieffer-Heeger Chain with Periodic Hopping Modulation
- URL: http://arxiv.org/abs/2405.04562v1
- Date: Tue, 7 May 2024 15:07:47 GMT
- Title: Topology and $\mathcal{PT}$ Symmetry in a Non-Hermitian Su-Schrieffer-Heeger Chain with Periodic Hopping Modulation
- Authors: Surajit Mandal, Satyaki Kar,
- Abstract summary: We study the effect of periodic hopping modulation on a Su-Schrieffer-Heeger chain that exhibits non-Hermiticity.
In particular, this paper is engaged with hopping periodicities of 2, 4 and 8 lattice spacings.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study the effect of periodic hopping modulation on a Su-Schrieffer-Heeger (SSH) chain that exhibits non-Hermiticity in presence of an onsite staggered imaginary potential. This dissipative, non-Hermitian (NH) extension amply modifies the features of the topological trivial phase (TTP) and the topological nontrivial phase (TNP) of the SSH chain. Though a weak potential can respect the parity-time ($\mathcal{PT}$) symmetry keeping the energy eigenvalues real, a strong potential breaks $\mathcal{PT}$ conservation leading to imaginary end state and complex bulk state energies in the system. Furthermore for large commensurate periodicity of the hopping, in-gap states appear that take either purely real or purely imaginary eigenvalues depending on the strenth of both NH potential and hopping modulation. In particular, this paper is engaged with hopping periodicities of 2, 4 and 8 lattice spacings. The localization of end states and in-gap states at the boundaries are investigated for those hopping periodicities. Though we find that topology and $\mathcal{PT}$ symmetry are not very directly connected, distinguishing distribution of $\mathcal{PT}$ broken and unbroken phases are clearly observed within TNP and TTP in our systems.
Related papers
- Emergence of non-Abelian SU(2) invariance in Abelian frustrated
fermionic ladders [37.69303106863453]
We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette.
Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry.
At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
arXiv Detail & Related papers (2023-05-11T15:57:27Z) - Measurement phase transitions in the no-click limit as quantum phase
transitions of a non-hermitean vacuum [77.34726150561087]
We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians.
We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
arXiv Detail & Related papers (2023-01-18T09:26:02Z) - Experimentally-realizable $\mathcal{PT}$ phase transitions in
reflectionless quantum scattering [0.0]
A class of above-barrier quantum-scattering problems is shown to provide an experimentally-accessible platform for studying $mathcalPT$-symmetric Schr"odinger equations.
These potentials are one-dimensional, inverted, and unstable and have the form $V(x) = - lvert xrvertp$ ($p>0$), terminated at a finite length or energy to a constant value as $xto pminfty$.
The signature of unbroken $mathcalPT$ symmetry is the existence of reflectionless propagating
arXiv Detail & Related papers (2022-09-12T17:30:58Z) - Non-zero momentum requires long-range entanglement [6.018940870331878]
We show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum.
The statement can also be generalized to fermion systems.
arXiv Detail & Related papers (2021-12-13T19:00:04Z) - Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized
rotational symmetry [85.36456486475119]
A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system.
Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
arXiv Detail & Related papers (2021-11-24T15:50:22Z) - Topological properties in the non-Hermitian tetramerized
Su-Schrieffer-Heeger lattices [0.0]
We study the topological properties of the non-Hermitian Su-Schrieffer-Heeger (SSH) lattice.
By changing the lattice to a tetramerized non-Hermitian system, such imaginary potentials induce the nontrivial transition of the topological properties of the SSH system.
arXiv Detail & Related papers (2021-11-13T03:22:24Z) - Reservoir-assisted symmetry breaking and coalesced zero-energy modes in
an open PT-symmetric Su-Schrieffer-Heeger model [0.0]
We study a model consisting of a central $mathcalPT$-symmetric trimer with non-Hermitian strength parameter $gamma$ coupled to two semi-infinite Su-Schrieffer-Heeger leads.
We show the existence of two zero-energy modes, one of which is localized while the other is anti-localized.
arXiv Detail & Related papers (2021-08-04T09:43:38Z) - Spectrum of localized states in fermionic chains with defect and
adiabatic charge pumping [68.8204255655161]
We study the localized states of a generic quadratic fermionic chain with finite-range couplings.
We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
arXiv Detail & Related papers (2021-07-20T18:44:06Z) - Dynamical solitons and boson fractionalization in cold-atom topological
insulators [110.83289076967895]
We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities.
We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors.
Using a pumping argument, we show that it survives also for finite interactions.
arXiv Detail & Related papers (2020-03-24T17:31:34Z) - Transition Probabilities for Flavor Eigenstates of Non-Hermitian
Hamiltonians in the PT-Broken Phase [0.0]
We investigate the transition probabilities for the "flavor" eigenstates in the two-level quantum system.
We show that the diverging behavior of the transition probabilities is actually applicable to the gauge-transformed neutral-meson states.
We also present a brief review on the situation at the so-called exceptional point, where both the eigenvalues and eigenvectors of the Hamiltonian coalesce.
arXiv Detail & Related papers (2020-02-13T14:04:04Z) - Anisotropy-mediated reentrant localization [62.997667081978825]
We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems.
We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
arXiv Detail & Related papers (2020-01-31T19:00:01Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.