Zero-modes and thermodynamics of disordered ladders

Gogolin, Alexander O.; Nersesyan, A. A.; Tsvelik, A. M.; Yu, Lu

doi:10.1016/s0550-3213(98)00776-7

Cited by 291 publications

(685 citation statements)

References 38 publications

Supporting

Mentioning

670

Contrasting

Order By: Relevance

“…This is the known result that can be found in Ref. 20. Figure 2 illustrates the real part of charge conductivity Reσ ρ (x, ω) (in units of e 2 /h) as a function of ωl/v F calculated according to Eq.…”

Section: Resultssupporting

confidence: 79%

Transport properties for a Luttinger liquid wire with Rashba spin–orbit coupling and Zeeman splitting

Cheng

Zhou

2007

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

We study the transport properties for a Luttinger-liquid (LL) quantum wire in the presence of both Rashba spin-orbit coupling (SOC) and a weak external in-plane magnetic field. The bosonized Hamiltonian of the system with an externally applied longitudinal electric field is established. And then the equations of motion for the bosonic phase fields are solved in the Fourier space, with which the both charge and spin conductivities for the system are calculated analytically based on the linear response theory. Generally, the ac conductivity is an oscillation function of the strengths of electron-electron interaction, Rashba SOC and magnetic field, as well as the driving frequency and the measurement position in the wire. Through analysis with some examples it is demonstrated that the modification on the conductivity due to electron-electron interactions is more remarkable than that due to SOC, while the effects of SOC and Zeeman splitting on the conductivity are very similar. The spin-polarized conductivities for the system in the absence of Zeeman effect or SOC are also discussed, respectively. The ratio of the spin-polarized conductivities σ ↑ /σ ↓ is dependent of the electron-electron interactions for the system without SOC, while it is independent of the electron-electron interactions for the system without Zeeman splitting.

show abstract

Section: Resultssupporting

confidence: 79%

Transport properties for a Luttinger liquid wire with Rashba spin–orbit coupling and Zeeman splitting

Cheng

Zhou

2007

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

show abstract

“…One dimensional systems are notoriously strongly correlated due to the limited phase space for scattering. The non-interacting ground state is immediately destroyed by interactions, forming a Luttinger liquid (LL) in many instances [8,9], and described by critical phenomena of collective modes with anomalous (non-integer) power-law dependence of correlation functions.Quantum quenches in Luttinger liquids have been addressed by several authors [10][11][12][13][14][15][16][17]. However, it is not clear to what extent the Luttinger liquid (LL) picture, which is a genuine low energy description, is applicable under non-equilibrium circumstances [17].…”

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Linear quantum quench in the Heisenberg XXZ chain: Time-dependent Luttinger-model description of a lattice system

2013

View full text Add to dashboard Cite

We study variable-rate linear quenches in the anisotropic Heisenberg (XXZ) chain, starting at the XX point. This is equivalent to swithcing on a nearest neighbour interaction for hard-core bosons or an interaction quench for free fermions. The physical observables we investigate are: the energy pumped into the system during the quench, the spin-flip correlation function, and the bipartite fluctuations of the z component of the spin in a box. We find excellent agreement between exact numerics (infinite system time-evolving block decimation, iTEBD) and analytical results from bosonization, as a function of the quench time, spatial coordinate and interaction strength. This provides a stringent and much-needed test of Luttinger liquid theory in a non-equilibrium situation.PACS numbers: 71.10. Pm,75.10.Jm,05.70.Ln, While it is difficult to study genuine non-equilibrium dynamics in solid state systems due to the presence of many relaxation channels (phonons, impurities, interactions etc.), cold atoms in optical lattices provide an ideal laboratory for non-equilibrium investigations due to the high degree of control over various dissipation mechanisms. Cold-atom experiments in the past decade have explored a wide variety of non-equilibrium quantum dynamics in previously inaccessible regimes [1,2]. This has also led to an increasing amount of theoretical activity [2,3]. Key issues include thermalization as well as equilibration and their relation to integrability [2], pumping beyond the adiabatic limit or quantum fluctuation relations [4], and universal near-adiabatic dynamics in quantum critical systems [2,3]. Linear quenches occuring over a finite time can interpolate between the more familiar limits of an instantaneous quench and an adiabatic sweep. Very recently, a few experiments have examined the response of many-body experiments to such finitetime quenches [5,6]. It is thus of vital current interest to address the dynamics under linear sweeps of system parameters such as interaction strength.The response of a system to an external perturbation depends sensitively on its spatial dimension, as famously demonstrated in the experiment of Ref. [7]. There, one dimensional interacting bosons did not reach thermalization within the experimental timescale, while their higher dimensional realizations did. One dimensional systems are notoriously strongly correlated due to the limited phase space for scattering. The non-interacting ground state is immediately destroyed by interactions, forming a Luttinger liquid (LL) in many instances [8,9], and described by critical phenomena of collective modes with anomalous (non-integer) power-law dependence of correlation functions.Quantum quenches in Luttinger liquids have been addressed by several authors [10][11][12][13][14][15][16][17]. However, it is not clear to what extent the Luttinger liquid (LL) picture, which is a genuine low energy description, is applicable under non-equilibrium circumstances [17]. For an abrupt interaction change, certain observables revealed universal LL ...

show abstract

“…Appendix A: Form-factor approach According to the form-factor approach 36,39,40 , the spectrum of lattice modulations is given by:…”

mentioning

confidence: 99%

Dynamical probing of a topological phase of bosons in one dimension

Torre

2013

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

We study the linear response to time-dependent probes of a symmetry-protected topological phase of bosons in one-dimension, the Haldane insulator (HI). This phase is separated from the ordinary Mott insulator (MI) and density-wave (DW) phases by continuous transitions, whose field theoretical description is here reviewed. Using this technique, we compute the absorption spectrum to two types of periodic perturbations and relate the findings to the nature of the critical excitations at the transition between the different phases. The HI-MI phase transition is topological and the critical excitations possess trivial quantum numbers: they correspond to particles and holes at zero momentum. Our findings are corroborated by a non-local mean-field approach, which allows us to directly relate the predicted spectrum to the known microscopic theory.

show abstract

Zero-modes and thermodynamics of disordered ladders

Cited by 291 publications

References 38 publications

Transport properties for a Luttinger liquid wire with Rashba spin–orbit coupling and Zeeman splitting

Transport properties for a Luttinger liquid wire with Rashba spin–orbit coupling and Zeeman splitting

Linear quantum quench in the Heisenberg XXZ chain: Time-dependent Luttinger-model description of a lattice system

Dynamical probing of a topological phase of bosons in one dimension

Contact Info

Product

Resources

About