Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9812237 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles

Tibor Antal A, Zoltàn Ràcz, Attila Rákos, Gunter Markus Schutz

Published May 1, 1999• 225 citations
arXivHTMLPDF

Abstract

We study the connection between magnetization transport and magnetization profiles in zero-temperature XX chains. The time evolution of the transverse magnetization m(x,t) is calculated using an inhomogeneous initial state that is the ground state at fixed magnetization but with m reversed from -m(0) for x<0 to m(0) for x>0. In the long-time limit, the magnetization evolves into a scaling form m(x,t)=Phi(x/t) and the profile develops a flat part (m=Phi=0) in the (x/t)<or=c(m(0)) region. The flat region shrinks to zero if m(0)-->1/2 while it expands with the maximum velocity c(0)=1 for m(0)-->0. The states emerging in the scaling limit are compared to those of a homogeneous system where the same magnetization current is driven by a bulk field, and we find that the expectation values of various quantities (energy, occupation number in the fermionic representation) agree in the two systems.

DOI
10.1103/physreve.59.4912

Related papers

Magnetization dynamics in the XX spin chain model via multiparticle state

Saptorshi Ghosh, Manvendra Singh, Suhas Gangadharaiah

We consider a multiparticle fermionic state to study the magnetization dynamics in an XX spin chain model. The advantage this state provides is the freedom in choosing the initial magnetization profile at each spin site. We characterize the $t=0$ properties of this state, in particular, the probability for the state to have $n$ fermions, fidelity, the two-point and the four-point correlators, and spin-spin correlations. The dynamics of the domain-wall state formed by considering the ground states with magnetizations ${m}_{0}$ and $\ensuremath{-}{m}_{0}$ in the left and right half of the chain, respectively, results in the growth of a flat plateau $(m=0)$ away from the origin. In contrast, the magnetization dynamics of the domain wall state initialized via the multiparticle state reveals the absence of such a region. Our studies of the particle-number fluctuation for the multiparticle state with all sites having identical magnetization reveals linear dependence with respect to the system size, as opposed to the $lnl$ dependence which is obtained for the ground state with the same magnetization.

Physical review. B./Physical review. B•Oct 29, 2021•1 citation

Dynamic scaling of fronts in the quantum XX chain

Viktória Hunyadi, Zoltàn Ràcz, L. Sasvári

The dynamics of the transverse magnetization in the zero-temperature XX chain is studied with emphasis on fronts emerging from steplike initial magnetization profiles. The fronts move with fixed velocity and display a staircase like internal structure whose dynamic scaling is explored both analytically and numerically. The front region is found to spread with time subdiffusively with the height and the width of the staircase steps scaling as t(-1/3) and t(1/3), respectively. The areas under the steps are independent of time; thus the magnetization relaxes in quantized "steps" of spin flips.

arXiv:cond-mat/0312250•Physical Review E•Jun 2, 2004•94 citations

Scaling and front dynamics in Ising quantum chains

Thierry Platini, Dragi Karevski

We study the relaxation behaviour of the quantum Ising chain, focusing our attention onto the non-equilibrium dynamics of the transverse magnetization. The initial states, from which the magnetization relaxes, are product states such as those generated by setting in contact several systems, each initially equilibrated at a given temperature. Due to the free fermionic structure of the chain, the dynamics of the transverse magnetization is easily expressed in a compact form. In the completely factorized initial state, corresponding to a situation where all the spins are thermalized independently, we obtain in the scaling limit the Green function associated to the transverse magnetization. The relaxation behaviour is also considered in the system-bath case, where part of the chain called the system is thermalized at a temperature Ts and the remaining part is at a temperature Tb. The magnetization profiles show a scaling behaviour. Moreover, in the extreme case Tb=∞ and Ts=0, it is shown that the magnetization relaxes in quantized steps in the strong transverse field region.

•Jan 1, 2005•34 citations

Nonequilibrium Dynamics due to Magnetization Transport in Transverse Ising Chain

Sirshendu Bhattacharyya, Subinay Dasgupta

We study the dynamics caused by transport of transverse magnetization in one dimensional transverse Ising chain at zero temperature. We observe that a class of initial states in fermionic momentum-space produce spatial variation in transverse magnetization. Starting from such a state, we obtain the transverse magnetization analytically and then observe its dynamics in presence of a homogeneous constant field $\Gamma$. In contradiction with general expectation, whatever be the strength of the field, the magnetization of the system does not become homogeneous even after infinite time. In each site, the dynamics is associated with oscillations having two different timescales. The envelope of the larger timescale oscillation decays algebraically having an exponent which is universal for the entire class of such initial states. Signature of quantum criticality is also embedded in the dynamics in two aspects : Behavioral change shown by the frequency of large timescale oscillation at any site and the corresponding magnetization at infinity when they cross the quantum critical point.

•Dec 13, 2016•0 citations

Finite size scaling and crossover phenomena: the XY chain in a transverse field at zero temperature

Raimundo R. dos Santos, Robin B. Stinchcombe

The scaling theory of finite size effects in the limiting bulk behaviour is extended to treat crossover phenomena. The method is used to study quantum critical phenomena in the XY chain in a transverse field at zero temperature, through the scaling of the longitudinal susceptibilities and of the energy gaps between the ground and two first excited states. As expected, no abrupt change in critical exponents is observed for small anisotropy. Because of the finiteness of the system, but the limiting isotropic and anisotropic regions display quite distinct critical behaviour, in good agreement with known results. Another interesting result obtained is that the two energy gaps examined vanish at the critical line with the same critical exponent.

Journal of Physics A Mathematical and General•Oct 1, 1981•20 citations

Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics

Márton Kormos

We investigate the non-equilibrium dynamics of the transverse field quantum Ising chain evolving from an inhomogeneous initial state given by joining two macroscopically different semi-infinite chains. We obtain integral expressions for all two-point correlation functions of the Jordan--Wigner Majorana fermions at any time and for any value of the transverse field. Using this result, we analytically compute the profiles of various physical observables in the space-time scaling limit and show that they can be obtained from a hydrodynamic picture based on ballistically propagating quasiparticles. Going beyond the hydrodynamic limit, we analyze the approach to the non-equilibrium steady state and find that the leading late time corrections display a lattice effect. We also study the fine structure of the propagating fronts which are found to be described by the Airy kernel and its derivatives. Near the front we observe the phenomenon of energy back-flow where the energy locally flows from the colder to the hotter region.

arXiv:1704.03744•SciPost Physics•Sep 8, 2017•91 citations
We study the connection between magnetization transport and magnetization profiles in zero-temperature XX chains. The time evolution of the transverse magnetization m(x,t) is calculated using an inhomogeneous initial state that is the ground state at fixed magnetization but with m reversed from -m(0) for x<0 to m(0) for x>0. In the long-time limit, the magnetization evolves into a scaling form m(x,t)=Phi(x/t) and the profile develops a flat part (m=Phi=0) in the (x/t)<or=c(m(0)) region. The flat region shrinks to zero if m(0)-->1/2 while it expands with the maximum velocity c(0)=1 for m(0)-->0. The states emerging in the scaling limit are compared to those of a homogeneous system where the same magnetization current is driven by a bulk field, and we find that the expectation values of various quantities (energy, occupation number in the fermionic representation) agree in the two systems.
We consider a multiparticle fermionic state to study the magnetization dynamics in an XX spin chain model. The advantage this state provides is the freedom in choosing the initial magnetization profile at each spin site. We characterize the t=0t=0t=0 properties of this state, in particular, the probability for the state to have nnn fermions, fidelity, the two-point and the four-point correlators, and spin-spin correlations. The dynamics of the domain-wall state formed by considering the ground states with magnetizations m0{m}_{0}m0​ and $\ensuremath{-}{m}_{0}$ in the left and right half of the chain, respectively, results in the growth of a flat plateau (m=0)(m=0)(m=0) away from the origin. In contrast, the magnetization dynamics of the domain wall state initialized via the multiparticle state reveals the absence of such a region. Our studies of the particle-number fluctuation for the multiparticle state with all sites having identical magnetization reveals linear dependence with respect to the system size, as opposed to the lnllnllnl dependence which is obtained for the ground state with the same magnetization.
The dynamics of the transverse magnetization in the zero-temperature XX chain is studied with emphasis on fronts emerging from steplike initial magnetization profiles. The fronts move with fixed velocity and display a staircase like internal structure whose dynamic scaling is explored both analytically and numerically. The front region is found to spread with time subdiffusively with the height and the width of the staircase steps scaling as t(-1/3) and t(1/3), respectively. The areas under the steps are independent of time; thus the magnetization relaxes in quantized "steps" of spin flips.
We study the relaxation behaviour of the quantum Ising chain, focusing our attention onto the non-equilibrium dynamics of the transverse magnetization. The initial states, from which the magnetization relaxes, are product states such as those generated by setting in contact several systems, each initially equilibrated at a given temperature. Due to the free fermionic structure of the chain, the dynamics of the transverse magnetization is easily expressed in a compact form. In the completely factorized initial state, corresponding to a situation where all the spins are thermalized independently, we obtain in the scaling limit the Green function associated to the transverse magnetization. The relaxation behaviour is also considered in the system-bath case, where part of the chain called the system is thermalized at a temperature Ts and the remaining part is at a temperature Tb. The magnetization profiles show a scaling behaviour. Moreover, in the extreme case Tb=∞ and Ts=0, it is shown that the magnetization relaxes in quantized steps in the strong transverse field region.
We study the dynamics caused by transport of transverse magnetization in one dimensional transverse Ising chain at zero temperature. We observe that a class of initial states in fermionic momentum-space produce spatial variation in transverse magnetization. Starting from such a state, we obtain the transverse magnetization analytically and then observe its dynamics in presence of a homogeneous constant field Γ\GammaΓ. In contradiction with general expectation, whatever be the strength of the field, the magnetization of the system does not become homogeneous even after infinite time. In each site, the dynamics is associated with oscillations having two different timescales. The envelope of the larger timescale oscillation decays algebraically having an exponent which is universal for the entire class of such initial states. Signature of quantum criticality is also embedded in the dynamics in two aspects : Behavioral change shown by the frequency of large timescale oscillation at any site and the corresponding magnetization at infinity when they cross the quantum critical point.
The scaling theory of finite size effects in the limiting bulk behaviour is extended to treat crossover phenomena. The method is used to study quantum critical phenomena in the XY chain in a transverse field at zero temperature, through the scaling of the longitudinal susceptibilities and of the energy gaps between the ground and two first excited states. As expected, no abrupt change in critical exponents is observed for small anisotropy. Because of the finiteness of the system, but the limiting isotropic and anisotropic regions display quite distinct critical behaviour, in good agreement with known results. Another interesting result obtained is that the two energy gaps examined vanish at the critical line with the same critical exponent.
We investigate the non-equilibrium dynamics of the transverse field quantum Ising chain evolving from an inhomogeneous initial state given by joining two macroscopically different semi-infinite chains. We obtain integral expressions for all two-point correlation functions of the Jordan--Wigner Majorana fermions at any time and for any value of the transverse field. Using this result, we analytically compute the profiles of various physical observables in the space-time scaling limit and show that they can be obtained from a hydrodynamic picture based on ballistically propagating quasiparticles. Going beyond the hydrodynamic limit, we analyze the approach to the non-equilibrium steady state and find that the leading late time corrections display a lattice effect. We also study the fine structure of the propagating fronts which are found to be described by the Airy kernel and its derivatives. Near the front we observe the phenomenon of energy back-flow where the energy locally flows from the colder to the hotter region.