Research Project PNIIIP4IDPCE20160032



Team:

Prof. Cătălin Pașcu Moca (Oradea, România)
Prof. Balázs Dóra (Budapest, Hungary) Prof. Gergely Zaránd (Budapest, Hungary) Dr. Răzvan Chirla (Oradea, România) Raluca Loredana Magyar (Oradea, România) Diana Maria Borodi (Oradea, România)


Summary:

The rapid development of laboratory techniques (in the field of trapped ultracold atoms and quantum dots) has opened the doors to experimental studies on how (open or closed) quantum systems thermalize. By means of optical lattices and Feschbach resonances, a wide range of Hamiltonians can be realized in practice to perform quantum simulations under nonequilibrium conditions. Being related to basic principles of statistical mechanics, the issues of thermalization and relaxation are of fundamental interest. Here we propose to investigate the nonequilibrium dynamics of a broad range of systems, discrete and continuous lattice models, as well as quantum impurity models, following a quantum quench. We would like to address important questions such as: Under what conditions do systems thermalize ? How is the thermal state approached ? These questions are not only of fundamental interest, but addressing the nonequilibrium time evolution of closed or almost closed interacting quantum systems is of primary importance for applications such as quantum cryptography, quantum simulations or quantum computations. Our main motivation comes from the observation that capturing the steady state correctly is hard, since the time scale covered by the present analytical and numerical methods is much smaller than the timescale for the relaxation processes. We are planning to study quantum quenches in models such as the sineGordon or the Luttinger liquid, and the realtime dynamics in quantum impurity systems. To reach these specific scientific goals, we are planning to develop new methods capable to investigate the longtime limit of prethermalized states, and to capture the evolution of entanglement following a quench. Here we have in mind the construction of an extended semiclassical approach, the development of a new TEBD code and and extension of our FlexibleDMNRG code to time dependent processes.


Results:

Publications with ISI impact factor:
1. B. Dora, M. A. Werner, C. P. Moca, Information scrambling at an impurity quantum critical point, Phys. Rev. B 96, 155116 (2017) (IF=3.8).
2. C. P. Moca, M. Kormos, G. Zarand, Hybrid Semiclassical Theory of Quantum Quenches in OneDimensional Systems, Phys. Rev. Lett 119, 100603 (2017) (IF=8.4).
3. C. P. Moca, C. Mora, I. Weymann, G. Zarand, Noise of a chargeless Fermi liquid, Phys. Rev. Lett. 120, 016803 (2018) (IF=8.4).
4. I. Weymann, R. Chirla, P. Trocha, C. P. Moca, The SU(4) Kondo effect in double quantum dots with ferromagnetic leads, Phys. Rev. B 97, 085404 (2018) (IF=3.8).
5. M. KanaszNagy, Y. Ashida, T. Shi, C. P. Moca, T. N. Ikeda, S. Folling, J. I. Cirac, G. Zarand, E. A. Demler, Exploring the Kondo model in and out of equilibrium with alkalineearth atoms, Phys. Rev. B 97, 155156 (2018) (IF=3.8).
6. M. Kormos, C. P. Moca, G. Zarand, Semiclassical theory of front propagation and front equilibration following an inhomogeneous quantum quench, Phys. Rev. E 98, 032105 (2018) (IF=2.3).
7. B. Dora, B. Hetenyi, C. P. Moca, Statistics and dynamics of the center of mass coordinate in a quantum liquid, Phys. Rev. Lett. 121, 056803 (2018) (IF=8.4).
8. M. Heyl, F. Pollmann, B. Dora, Detecting Equilibrium and Dynamical Quantum Phase Transitions in Ising Chains via OutofTimeOrdered Correlators, Phys. Rev. Lett. 121, 016801 (2018) (IF=8.4).
9. L. Oroszlany, B. Dora, J. Cserti, A. Cortijo, Topological and trivial magnetic oscillations in nodal loop semimetals, Phys. Rev. B 97, 205107 (2018) (IF=3.8).
Preprints and submitted articles:
1. I. Shapir, A. Hamo, S. Pecker, C. P. Moca, O. Legeza, G. Zarand, S. Ilani, Imaging the Wigner Crystal of Electrons in One Dimension, arXiv:1803.08523, submitted.
2. Z. Okvatovity, H. Yasuoka, M. Baenitz, F. Simon, B. Dora, Nuclear spinlattice relaxation time in TaP and the Knight shift of Weyl semimetals, arXiv:1806.08163, submitted.
3. B. Hetenyi, B. Dora, Finite size scaling around a metalinsulator transition from the polarization amplitude, arXiv:1810.10878, submitted.
Proceedings Publications:
1. C. P. Moca, A. Roman, M. Toderaș and R. Chirla, Triple dot system coupled to topological insulators: A Numerical Renormalization Group analysis of the SU(3) attractive Anderson model, AIP Conference Proceedings 1916, 030003 (2017).


Scientific Reports (RO):


Objectives and Expected Results:

The results of our research shall be published in international refereed journals such as the Physical Review or the Physical Review Letters, and we shall also present our achievements at national and international conferences. We are planning to publish on average 35 or even more papers/year. The projected results are within two main directions of research:
A) Global quenches in closed interacting models
In most physical systems integrability is violated, while integrable systems are expected to be fragile with respect to typical perturbations of the Hamiltonian. The system often evolves towards a 'prethermalized state', i.e., a state with many 'almost conserved' charges. The primary objective of the project is to develop a theoretical framework able to capture the decay of these prethermalized states. Recently, in a very interesting work [Rieger2011], an extension of the semiclassical method proposed originally by Sachdev and Young [Sachdev1997] was proposed for the study of quantum quenches in the transverse field Ising model. The basic idea of this method is that in a small quench, a dilute gas of pairs of quasiparticles is created. These quasiparticles move classically, and collide as hard balls in the limit of the universal Smatrix (thus, for example, in the sineGordon model, in the universal limit, the topological charges of the solitons/antisolitions involved into a collision are conserved). We shall go beyond the universal limit to include effects of the energy dependence of the scattering matrix. In this way, quantum scattering effects are included. Then, the full wave function can still be factorized into an orbital and a quantum part that describes the topological charges. We shall treat the 'charge' part of the semiclassical wave function completely quantum mechanically by means of a TEBDlike method, while treating the orbital motion semiclassically. We shall call this approach the extended semiclassical approach (ESC). The approach shall be applied to cold atomic systems, such as a coherently split onedimensional Bose liquid. After creating two parallel, identical onedimensional correlated Bose clouds, the atoms are released from the traps, and the clouds expand. After some time, the interference pattern of the overlapping clouds is imaged, and the fluctuations of the interference amplitude as well as the relative phase is analyzed and their full distribution function is obtained [Hofferberth2006, Gritsev2006]. We will investigate the effect of the interaction quench on the Bose cloud. The evolution of the relative phase of the two superfluids can be described by the sineGordon model which is also equivalent to the massive Thirring model describing Dirac fermions. We shall investigate the relative phase distribution between the condensates and compare experimental predictions with simulations. Furthermore, with the recent progress in measuring the entanglement properties of a system [Islam2015] we shall focus on the entanglement entropy and mutual information of such systems. The most natural question we may ask is: What is the real space picture of the entanglement spreading ? We can give an answer to this question by measuring entanglement in a tripartite systems. In this context, the Renyi entropy of index ½ (logarithmic negativity), would provide evidence of a local, real space picture of entanglement spreading in time. This ESC method is also suitable for computing the outofequilibrium evolution of the correlation functions. We shall compute the averages for the one and twopoint correlation functions, as their spatial integration is directly related to the contrast of the interference fringes. We shall also develop a nonabelian TEBD and use it to investigate very basic nonintegrable quantum systems such as the spin S=1 antiferromagnetic Heisenberg chain. By building explicitely symmetries into our TEBD approach, the time scale covered will significantly increase. Moreover, such a system possesses the Haldane gap in the energy spectrum, thus it is suitable for being studied with the ESC approach. In this way we can make a comparison between the two methods and study their limitations. The ESC approach discussed so far is suitable to investigate quenches in gapped phases of prototypical models. On the other hand, various onedimensional (1D) interacting systems such as interacting 1D bosons or spin chains [Giamarchi2004], present gapless phases for which the Luttinger liquid ubiquitously describes their effective low energy behavior. We plan to study Luttinger liquids under nonequilibrium circumstances with special emphasis on the entanglement entropy. So far most studies focused mainly on the realspace partitioning of a system, but other ways of partitioning are equally fruitful. In particular, partitioning in momentumspace is natural, as various instabilities and phase transitions occur by coupling distinct regions in momentumspace together via interactions. For example, Cooper pairs are made of particles with opposite momentum and give rise to superconductivity. In one dimension, Luttinger liquids (LLs), which host many interesting phenomena such as spincharge separation, charge fractionalization, and nonFermi liquid behaviour, appear after coupling right and leftmoving fermions together. Therefore, a momentumspace partitioning offers a unique perspective on the structure of manyparticle wavefunctions. We will combine momentumspace entanglement and quantum quenches in a LL and in other 1D systems. Using bosonization and numerical exact diagonalization, we will evaluate the entanglement spectrum and investigate its universal properties such as the entanglement gap, or the corresponding entanglement entropies.
B) Quantum quenches in quantum impurity systems
We shall address the problem of real time dynamics in quantum impurity systems under a quantum quench change in the system Hamiltonian. The time dependent numerical renormalization group (TDDMNRG) would offer the possibility of investigating nonpertubatively the time dependence of local observables in interacting quantum impurity models following a quantum quench, as well as the linear transport properties such as the conductance [Anders2008, Nghiem2014]. In contrast to other approaches, TDDMNRG allows to derive accurate transport properties at finite temperatures. In this way, the time evolution of quantities such as the thermopower or thermal conductance are accessible [Chirla2014]. Furthermore, the method can be extended to correlated lattice models such as the Kondo lattice, or the Hubbard model or even applied to HubbardBose systems. Most of the theoretical work so far was focused on understanding static transport quantities [Anders2008], such as the conductance, while the spectral properties of the system, as well as the dynamical quantities were most of the time not investigated. Our primary purpose here is to construct a timedependent numerical renormalization group scheme for the evaluation of both dynamical and static correlations under sudden changes of the system Hamiltonian, and to implement it into the FlexibleDMNRG package. This approach must be able to explicitly use the symmetries of the system. Once the code is available, we shall investigate the nonequilibrium spectral properties and the time evolution of static quantities characterizing the Kondo systems. Here we have in mind a thorough investigation of both Kondo and Anderson models, when one of the system parameters, such as the exchange coupling J, or the external magnetic field B are suddenly changed. We shall address the effect of the nonequilibrium on thermal quantities as well. From a technical point our development will supplement the list of other methods used to address quantum fluctuations problems under nonequilibrium conditions, such as the time dependent density matrix renormalization group (TDDMRG) method [Fuehringer2008, Schollwock2005], or the quantum Monte Carlo method for nonequilibrium problems [Werner2009].


References: 
[Anders2008] F. B. Anders, et. al., Phys. Rev. Lett. 100, 086809 (2008).
[Chirla2014] R. Chirla, I.V. Dinu, V.Moldoveanu and C.P. Moca , Phys. Rev. B 90, 195108 (2014).
[Fuehringer2008] M. Fuehringer, et.al., Ann. Phys. 17, 922 (2008).
[Giamarchi2004] Quantum Physics in One dimension (Oxford University Press, Oxford, 2004).
[Gritsev2006] V. Gritsev, et. al., Nature Physics 2, 705 (2006).
[Hofferberth2007] S. Hofferberth, et. al., Nature 449, 324327 (2007).
[Islam2015] R. Islam, et. al., Nature 528, 77 (2015).
[Nghiem2014] H. T. M. Nghiem , et. al., Phys. Rev. B 90, 035129 (2014).
[Rieger2011] H. Rieger, et. al., Phys. Rev. B 84, 165117 (2011).
[Sachdev1997] S. Sachdev and A. P. Young, Phys. Rev. Lett. 78, 2220 (1997).
[Schollwock2011] U. Schollwock, Annals of Physics 326, 96 (2011).
[Werner2009] P. Werner, T. Oka and A. J. Millis, Phys. Rev. B 79, 035320 (2009).


Last updated: December 3, 2018

The results of our research shall be published in international refereed journals such as the Physical Review or the Physical Review Letters, and we shall also present our achievements at national and international conferences. We are planning to publish on average 35 or even more papers/year.