Time evolution of the haldane state after a quantum quench

• Autorzy: Woźniak D. , Drzewiński A. , Kamieniarz G.
• Języki publikacji: EN

Abstrakty

EN

In the framework of the Matrix Product States representation the effect of a sudden quench of the uniaxial anisotropy on the time evolution of the Haldane state has been investigated. The existence of the non-vanishing string correlations in the limit of a large distance in the Haldane phase has been verified. The overlap of the initial and time-evolved states, the so-called Loschmidt echo, has been investigated.

Słowa kluczowe

EN

computational statistical mechanics; ground state; dynamical properties of magnetic chains

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 4
• Strony: 151--156
• Opis fizyczny: Bibliogr. 13 poz., rys.

Twórcy

autor

Woźniak D.

• Institute of Physics, University of Zielona Góra, Zielona Góra, Poland

autor

Drzewiński A.

• Institute of Physics, University of Zielona Góra, Zielona Góra, Poland

autor

Kamieniarz G.

• Faculty of Physics, A. Mickiewicz University, Poznań, Poland

Bibliografia

• [1] Bloch I., Dalibard J., Zwerger W., Many-body physics with ultracold gases, Rev. Mod. Phys. 2008, 80, 885- 964; Simon J., Bakr W.S., Ma R., Tai M.E., Preiss P.M., Greiner M., Quantum simulation of antiferromagnetic spin chains in an optical lattice, Nature 2011, 472, 307-312.
• [2] Haldane F.D.M., Nonlinear field theory of large-spin Heisenberg antiferromagnets: semiclassically quantized solitons of the one-dimensional easy-axis Néel state, Phys. Rev. Lett. 1983, 50, 1153-1156; Haldane F.D.M., Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model, Phys. Lett. A 1983, 93, 464-468.
• [3] Affleck I., Kennedy T., Lieb E.H., Tasaki H., Rigorous results on valence-bond ground states in antiferromagnets, Phys. Rev. Lett. 1987, 59, 799-802.
• [4] White S.R., Huse D.A., Numerical renormalization-group study of low-lying eigenstates of the antiferromagnetic S=1 Heisenberg chain, Phys. Rev. B 1993, 48, 3844-3852.
• [5] den Nijs M., Rommelse K., Preroughening transitions in crystal surfaces and valence-bond phases in quantum spin chains, Phys. Rev. B 1989, 40, 4709-4734.
• [6] Chen W., Hida K., Sanctuary B.C., Ground-state phase diagram of S=1 XXZ chains with uniaxial single-ion-type anisotropy, Phys. Rev. B 2003, 67, 104401.
• [7] Őstlund S., Rommer S., Thermodynamic limit of density matrix renormalization, Phys. Rev. Lett. 1995, 75, 3537-3540.
• [8] Pozsgay B., The dynamical free energy and the Loschmidt echo for a class of quantum quenches in the Heisenberg spin chain, J. Stat. Mech. 2013, 13, 10028.
• [9] Mazza L., Rossini D., Endres M., Fazio R., Out-of-equilibrium dynamics and thermalization of string order, Phys. Rev. B 2014, 90, 020301.
• [10] Schollwöck U., The density-matrix renormalization group, Rev. Mod. Phys. 2005, 77, 259-315; Schollwöck U., The density-matrix renormalization group in the age of matrix product states, Annals of Physics 2011, 326, 96-192.
• [11] Verstraete F., Cirac K., Matrix product states represent ground states faithfully, Phys. Rev. B 2006, 73, 094423; Verstraete F., Murg V., Cirac K., Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems, Adv. Phys. 2008, 57, 143-224.
• [12] Woźniak D., Drzewiński A., Kamieniarz G., Matrix-product states for the Ising model in a transverse field, Acta Physicae Superficierum 2012, 12, 187-194.
• [13] Alcaraz F.C., Hatsugai Y., String correlation functions in the anisotropic spin-1 Heisenberg chain, Phys. Rev. B 1992.