Quantum spin chains with multiple dynamics

Abstract

Many-body systems with multiple emergent time scales arise in various contexts, including classical critical systems, correlated quantum materials, and ultra-cold atoms. We investigate such non-trivial quantum dynamics in a new setting: a spin-1 bilinear-biquadratic chain. It has a solvable entangled groundstate, but a gapless excitation spectrum that is poorly understood. By using large-scale DMRG simulations, we find that the lowest excitations have a dynamical exponent z that varies from 2 to 3.2 as we vary a coupling in the Hamiltonian. We find an additional gapless mode with a continuously varying exponent 2 ≤ z < 2.7, which establishes the presence of multiple dynamics. In order to explain these striking properties, we construct a continuum wavefunction for the groundstate, which correctly describes the correlations and entanglement properties. We also give a continuum parent Hamiltonian, but show that additional ingredients are needed to capture the excitations of the chain. By using an exact mapping to the non-equilibrium dynamics of a classical spin chain, we find that the large dynamical exponent is due to subdiffusive spin motion. Finally, we discuss the connections to other spin chains and to a family of quantum critical models in 2d.It is common for many-body quantum systems to possess multiple time-scales that determine the low-energy dynamics. In a gapless system, the dynamics will be characterized by the dispersion relation of the excited states (quasiparticles need not exist), E = Ak z , where k is the wavevector of the mode and z the dynamical exponent. Different modes can have different z exponents. For instance, a metal near a quantum critical point can have different dispersions for the electrons and the various order parameter fluctuations [1][2][3][4][5][6]. However, this phenomenon has been far less studied in other types of systems. Many studies have examined simpler systems, such as models described by relativistic conformal field theories having z = 1, which enjoy additional symmetries that constrain the dynamics [3,7,8].In this work, we reveal multiple dynamical exponents in a new setting: a strongly correlated 1d spin system. Further, these exponents will be shown to vary continuously as a function of a coupling in the Hamiltonian. The spin 1 quantum spin chain in question is a generalization of the so-called Motzkin Hamiltonian introduced by Bravyi et al [9]. Its groundstate can be determined exactly but not its excitation spectrum. With the help of large-scale Density Matrix Renormalization Group (DMRG) simulations, we discover low lying excitations with different dynamical exponents. In order to gain insight in the low-lying spectrum we determine a continuum version of the groundstate, and find a parent Hamiltonian. The latter possesses an excitation spectrum that is distinct from the spin chain but can provide useful insight into the construction of the full low energy field theory. This illustrates how a given groundstate can have starkly different excitations, and offers some g...

Hybridization Dynamics in CeCoIn5 Revealed by Ultrafast Optical Spectroscopy

“…While the relaxation rate shows a clear reduction starting at around T † ≈ 120 K and continuing below T * ≈ 55 K, it becomes strongly fluence-dependent below T * . These seem to be in exact accordance with the observations in ARPES [4] and transport experiments [8], respectively. We argue that the fluence-dependent relaxation indicates a nonlinear effect which may be ascribed to bimolecular recombination of excited quasiparticles across a narrow indirect hybridization gap associated with the formation of coherent heavy electrons on the Kondo lattice, while the fluence-independent relaxation implies the (indirect) gap closing above T * and should originate from the effect of precursor hybridization fluctuations.…”

“…It has been further confirmed in the scanning tunneling microscopy/spectroscopy investigations which revealed an unusual quantum critical E/T scaling in the local conductance below 60 K [11]. On the other hand, recent ARPES experiments [4][5][6][7] reported signatures of hybridization between f and conduction electrons well above 100 K, at which temperature f electrons are believed to be still localized. Fourier transform infrared spectroscopy (FTIR) also revealed a direct gap emerging below certain temperature above T * , although the exact onset temperatures differ in various experiments [12][13][14].…”

“…It is generally believed that T * marks the onset of collective hybridization between localized f moments and conduction electrons, causing the emergence of heavy electrons at lower temperatures [3]. However, recent angle-resolved photoemission spectroscopy (ARPES) measurements seem to indicate the presence of hybridization already at much higher temperatures and no peculiar signatures were observed across T * [4][5][6][7]. This leads to a puzzling contradiction of interpretation among different probes and prevents a consistent understanding of the heavy fermion physics.…”

Haldane topological orders in Motzkin spin chains

“…Finally we underline that, in future works, it would be very interesting to study the gapped regimes in the fermionic version of the s = 3/2 Fredkin model where exotic Haldane regimes can take place [41]. Note added: After the submission of this paper, two papers appeared on arXiv where a Motzkin spin chain is considered introducing a field theory approach to study certain observables and entanglement measures [42]. We think that addressing with such approach the properties discussed in the present paper would be very interesting, in particular the discussion on the BKT nature of the transition at t = 1.…”

Large Enhancement of Thermoelectric Efficiency Due to a Pressure-Induced Lifshitz Transition in SnSe

“…[33][34][35] and hence tend to stabilise the highersymmetry Cmcm phase [34][35][36][37][38]. (Note here that the structural transition from P nma to Cmcm occurs at ∼10 GPa [34,35,39], much higher than the present pressure range.) Thus, the b/c value can be a key factor for raising the energy of the valence band along the Γ-Y line and achieving the four-valley structure.…”