scholarly journals Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

2019 ◽  
Vol 7 (2) ◽  
Author(s):  
Grégoire Misguich ◽  
Nicolas Pavloff ◽  
Vincent Pasquier
Keyword(s):  
Domain Wall ◽  
Entanglement Entropy ◽  
Spin Correlation ◽  
Quantitative Agreement ◽  
Isotropic Point ◽  
Density Matrix Renormalization ◽  
Energy Current ◽  
Quantum Chain ◽  
Xxz Chain ◽  
Long Time

We study the dynamics of a spin-\frac{1}{2}12 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization (xx, yy and zz components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schrödinger equation is used to construct a variational solution capturing several aspects of the problem.

scholarly journals Entanglement signatures of emergent Dirac fermions: Kagome spin liquid and quantum criticality

2018 ◽  
Vol 4 (11) ◽  
pp. eaat5535 ◽  
Author(s):  
Wei Zhu ◽  
Xiao Chen ◽  
Yin-Chen He ◽  
William Witczak-Krempa
Keyword(s):  
Entanglement Entropy ◽  
Quantum Critical Point ◽  
Quantum Spin ◽  
Spin Liquid ◽  
Dirac Fermions ◽  
Spin Liquids ◽  
Density Matrix Renormalization ◽  
Dirac Semimetal ◽  
A Charge ◽  
Aharonov Bohm

Quantum spin liquids (QSLs) are exotic phases of matter that host fractionalized excitations. It is difficult for local probes to characterize QSL, whereas quantum entanglement can serve as a powerful diagnostic tool due to its nonlocality. The kagome antiferromagnetic Heisenberg model is one of the most studied and experimentally relevant models for QSL, but its solution remains under debate. Here, we perform a numerical Aharonov-Bohm experiment on this model and uncover universal features of the entanglement entropy. By means of the density matrix renormalization group, we reveal the entanglement signatures of emergent Dirac spinons, which are the fractionalized excitations of the QSL. This scheme provides qualitative insights into the nature of kagome QSL and can be used to study other quantum states of matter. As a concrete example, we also benchmark our methods on an interacting quantum critical point between a Dirac semimetal and a charge-ordered phase.

scholarly journals LONG-TIME RELAXATION ON SPIN LATTICE AS A MANIFESTATION OF CHAOTIC DYNAMICS

2004 ◽  
Vol 18 (08) ◽  
pp. 1119-1159 ◽  
Author(s):  
BORIS V. FINE
Keyword(s):  
Correlation Functions ◽  
Time Scale ◽  
Inelastic Neutron Scattering ◽  
Spin Correlation ◽  
Inelastic Neutron ◽  
Theoretical Explanation ◽  
Characteristic Time Scale ◽  
Time Behavior ◽  
Intermediate Structure ◽  
Long Time

The long-time behavior of the infinite temperature spin correlation functions describing the free induction decay in nuclear magnetic resonance and intermediate structure factors in inelastic neutron scattering is considered. These correlation functions are defined for one-, two- and three-dimensional infinite lattices of interacting spins, both classical and quantum. It is shown that, even though the characteristic time-scale of the long-time decay of the correlation functions considered is non-Markovian, the generic functional form of this decay is either simple exponential or exponential multiplied by cosine. This work contains (i) the summary of the existing experimental and numerical evidence of the above asymptotic behavior; (ii) theoretical explanation of this behavior; and (iii) semi-empirical analysis of various factors discriminating between the monotonic and the oscillatory long-time decays. The theory is based on a fairly strong conjecture that, as a result of chaos generated by spin dynamics, a Brownian-like Markovian description can be applied to the long-time properties of ensemble average quantities on a non-Markovian time-scale. The formalism resulting from that conjecture can be described as "correlated diffusion in finite volumes."

scholarly journals Chiral order of spin-1/2 frustrated quantum spin chains

2001 ◽  
Vol 79 (11-12) ◽  
pp. 1587-1591 ◽  
Author(s):  
T Hikihara ◽  
M Kaburagi ◽  
H Kawamura
Keyword(s):  
Nearest Neighbor ◽  
Spin Correlation ◽  
Quantum Spin ◽  
Spontaneous Breaking ◽  
Group Method ◽  
Density Matrix Renormalization Group ◽  
Quantum Spin Chains ◽  
Chiral Phase ◽  
Density Matrix Renormalization ◽  
Xy Spin Chain

The ordering of the frustrated S = 1/2 XY spin chain with the competing nearest- and next-nearest-neighbor anti-ferromagnetic couplings, J1 and J2, is studied by using the density-matrix renormalization-group method. It is found that besides the well-known spin-fluid and dimer phases the chain exhibits a gapless "chiral" phase characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κl =SxlSyl+1 – Syl Sxl+1, whereas the spin correlation decays algebraically. The dimer phase is realized for 0.33 [Formula: see text] j = J2/J1 [Formula: see text] 1.26 while the chiral phase is realized for j [Formula: see text] 1.26. PACS No.: 75.25

Anomalous Long Time Tail Behavior of Spin-Spin Correlation in the Normal State ofTl2Ba2CuOy

1994 ◽  
Vol 73 (1) ◽  
pp. 197-200 ◽  
Author(s):  
Shinsaku Kambe ◽  
Hiroshi Yasuoka ◽  
Akihiko Hayashi ◽  
Yutaka Ueda
Keyword(s):  
Normal State ◽  
Spin Correlation ◽  
Tail Behavior ◽  
Long Time

scholarly journals Relaxation of the order-parameter statistics in the Ising quantum chain

2019 ◽  
Vol 7 (6) ◽  
Author(s):  
Mario Collura
Keyword(s):  
Probability Distribution ◽  
Ground State ◽  
Order Parameter ◽  
Classical Model ◽  
Transverse Field ◽  
Analytical Description ◽  
Spin Correlation ◽  
Local Order ◽  
Late Time ◽  
Quantum Chain

We study the out-of-equilibrium probability distribution function of the local order parameter in the transverse field Ising quantum chain. Starting from a fully polarised state, the relaxation of the ferromagnetic order is analysed: we obtain a full analytical description of the late-time stationary distribution by means of a remarkable relation to the partition function of a 3-states classical model. Accordingly, depending on the phase whereto the post-quench Hamiltonian belongs, the probability distribution may locally retain memories of the initial long-range order. When quenching deep in the broken-symmetry phase, we show that the stationary order-parameter statistics is indeed related to that of the ground state. We highlight this connection by inspecting the ground-state equilibrium properties, where we propose an effective description based on the block-diagonal approximation of the nn-point spin correlation functions.

Superconductivity and Magnetic Properties of the t–J Model of Cuprate Perovskites

1998 ◽  
Vol 12 (29n31) ◽  
pp. 3039-3041
Author(s):  
A. Sherman ◽  
M. Schreiber
Keyword(s):  
Spin Echo ◽  
Relaxation Times ◽  
Lattice Relaxation ◽  
Wave Theory ◽  
Spin Correlation ◽  
Quantitative Agreement ◽  
Spin Lattice Relaxation ◽  
Spin Lattice ◽  
Hole Spectrum ◽  
Temperature Dependences

We apply the spin-wave theory with the additional constraint of zero staggered magnetization to investigate the two-dimensional t–J model in the paramagnetic state in the ranges of hole concentrations 0.02 ≲ x ≲ 0.17 and temperatures T ≲ 100 K. In this region the hole spectrum is nonmetallic and contains a pseudogap with properties similar to those observed in Bi2212 photoemission. The calculated spin correlation length, susceptibility, spin-lattice relaxation times at the Cu and O sites and Cu spin-echo decay time are in qualitative and in some cases in quantitative agreement with experiment in underdoped YBa2Cu3O 6+y. The temperature dependences of these quantities are typical for the quantum disordered regime with a pseudogap in the spectrum of magnetic excitations. In the Eliashberg formalism the hole–magnon interaction was found to be unable alone to give rise to superconductivity. With inclusion of a moderate interaction with apex oxygen vibrations, high-T c 's are obtained for even frequency dx2-y2 pairing.

scholarly journals Coexistence of Different Scaling Laws for the Entanglement Entropy in a Periodically Driven System

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 6
Author(s):  
Tony J. G. Apollaro ◽  
Salvatore Lorenzo
Keyword(s):  
Ground State ◽  
Scaling Laws ◽  
Entanglement Entropy ◽  
Finite Size ◽  
Simultaneous Occurrence ◽  
Many Body ◽  
Periodically Driven ◽  
Quantum Ising Model ◽  
Long Time ◽  
Many Body Systems

The out-of-equilibrium dynamics of many body systems has recently received a burst of interest, also due to experimental implementations. The dynamics of observables, such as magnetization and susceptibilities, and quantum information related quantities, such as concurrence and entanglement entropy, have been investigated under different protocols bringing the system out of equilibrium. In this paper we focus on the entanglement entropy dynamics under a sinusoidal drive of the tranverse magnetic field in the 1D quantum Ising model. We find that the area and the volume law of the entanglement entropy coexist under periodic drive for an initial non-critical ground state. Furthermore, starting from a critical ground state, the entanglement entropy exhibits finite size scaling even under such a periodic drive. This critical-like behaviour of the out-of-equilibrium driven state can persist for arbitrarily long time, provided that the entanglement entropy is evaluated on increasingly subsytem sizes, whereas for smaller sizes a volume law holds. Finally, we give an interpretation of the simultaneous occurrence of critical and non-critical behaviour in terms of the propagation of Floquet quasi-particles.

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