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Register a new userMelting of the critical behavior of a Tomonaga-Luttinger liquid under dephasing
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Added by
Jean-Sebastien Bernier
Publication date
2020
fields
Physics
and research's language is
English
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Strongly correlated quantum systems often display universal behavior as, in certain regimes, their properties are found to be independent of the microscopic details of the underlying system. An example of such a situation is the Tomonaga-Luttinger liquid description of one-dimensional strongly correlated bosonic or fermionic systems. Here we investigate how such a quantum liquid responds under dissipative dephasing dynamics and, in particular, we identify how the universal Tomonaga-Luttinger liquid properties melt away. Our study, based on adiabatic elimination, shows that dephasing first translates into the damping of the oscillations present in the density-density correlations, a behavior accompanied by a change of the Tomonaga-Luttinger liquid exponent. This first regime is followed by a second one characterized by the diffusive propagation of featureless correlations as expected for an infinite temperature state. We support these analytical predictions by numerically exact simulations carried out using a number-conserving implementation of the matrix product states algorithm adapted to open systems.
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Low dimensional quantum magnets are interesting because of the emerging collective behavior arising from strong quantum fluctuations. The one-dimensional (1D) S = 1/2 Heisenberg antiferromagnet is a paradigmatic example, whose low-energy excitations, known as spinons, carry fractional spin S = 1/2. These fractional modes can be reconfined by the application of a staggered magnetic field. Even though considerable progress has been made in the theoretical understanding of such magnets, experimental realizations of this low-dimensional physics are relatively rare. This is particularly true for rare-earth based magnets because of the large effective spin anisotropy induced by the combination of strong spin-orbit coupling and crystal field splitting. Here, we demonstrate that the rare-earth perovskite YbAlO$_3$ provides a realization of a quantum spin S = 1/2 chain material exhibiting both quantum critical Tomonaga-Luttinger liquid behavior and spinon confinement-deconfinement transitions in different regions of magnetic field-temperature phase diagram.
In a one-dimensional (1D) system of interacting electrons, excitations of spin and charge travel at different speeds, according to the theory of a Tomonaga-Luttinger Liquid (TLL) at low energies. However, the clear observation of this spin-charge separation is an ongoing challenge experimentally. We have fabricated an electrostatically-gated 1D system in which we observe spin-charge separation and also the predicted power-law suppression of tunnelling into the 1D system. The spin-charge separation persists even beyond the low-energy regime where the TLL approximation should hold. TLL effects should therefore also be important in similar, but shorter, electrostatically gated wires, where interaction effects are being studied extensively worldwide.
We study both noncentrosymmetric and time-reversal breaking Weyl semimetal systems under a strong magnetic field with the Coulomb interaction. The three-dimensional bulk system is reduced to many mutually interacting quasi-one-dimensional wires. Each strongly correlated wire can be approached within the Tomonaga-Luttinger liquid formalism. Including impurity scatterings, we inspect the localization effect and the temperature dependence of the electrical resistivity. The effect of a large number of Weyl points in real materials is also discussed.
Using a Luttinger liquid theory we investigate the time evolution of the particle density of a one-dimensional spinful fermionic system with open boundaries and subject to a finite-duration quench of the inter-particle interaction. Taking into account also the turning on of an umklapp perturbation to the system Hamiltonian as a result of the quench, we study the possible formation of a Wigner molecule inside the system, focusing in particular on the sudden and adiabatic regimes. We show that the creation of this correlated state is essentially due to the propagation of light-cone perturbations through system which arise after both switching on and switching off the quenching protocol and that its behavior strongly depends on the quench duration.
We demonstrate that quantum-critical spin dynamics can be probed in high magnetic fields using muon-spin relaxation ($mu^{+}$SR). Our model system is the strong-leg spin ladder bis(2,3-dimethylpyridinium) tetrabromocuprate (DIMPY). In the gapless Tomonaga-Luttinger liquid phase we observe finite-temperature scaling of the $mu^{+}$SR $1/T_1$ relaxation rate which allows us to determine the Luttinger parameter $K$. We discuss the benefits and limitations of local probes compared with inelastic neutron scattering.
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