%0 Book Section %1 statphys23_0486 %A Nakamura, Y.N. %A Hatano, N.H. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K correlation dispersion hubbard length model relation statphys23 topic-8 xxz %T Non-Hermitian quantum mechanics of strongly correlated systems %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=486 %X We argue that the imaginary part of zeros of the dispersion relation of the elementary excitation of a quantum systems is equal to the inverse correlation length. We confirm the relation for the Hubbard model1 in the half-filled case and the S=1/2 antiferromagnetic XXZ chain2. In order to search zeros of the dispersion relation in the complex momentum space efficiently, we introduce a non-Hermitian generalization of quantum systems by adding an imaginary vector potential ig to the momentum operator3. We calculate a non-Hermitian critical point $g_c$ at which the energy gap between the ground state and the excited state vanishes and above which the ground-state energy becomes complex. We show numerical data of gc for the Heisenberg chain with nearest- and next-nearest-neighbor interactions. We also show that we can obtain the inverse correlation length of this model by extrapolating the finite-size estimates of $g_c$ to infinite systems. 1) Y. Nakamura and N. Hatano, in preparation.\\ 2) K. Okunishi, Y. Akutsu, N. Akutsu and T. Yamamoto, Phys. Rev. B 64 (2001) 104432.\\ 3) Y. Nakamura and N. Hatano, Physica B 378-380 (2006) 292; J. Phys. Soc. Jpn. 75 (2006) 114001.

@incollection{statphys23_0486, abstract = {We argue that the imaginary part of zeros of the dispersion relation of the elementary excitation of a quantum systems is equal to the inverse correlation length. We confirm the relation for the Hubbard model[1] in the half-filled case and the S=1/2 antiferromagnetic XXZ chain[2]. In order to search zeros of the dispersion relation in the complex momentum space efficiently, we introduce a non-Hermitian generalization of quantum systems by adding an imaginary vector potential ig to the momentum operator[3]. We calculate a non-Hermitian critical point $g_c$ at which the energy gap between the ground state and the excited state vanishes and above which the ground-state energy becomes complex. We show numerical data of gc for the Heisenberg chain with nearest- and next-nearest-neighbor interactions. We also show that we can obtain the inverse correlation length of this model by extrapolating the finite-size estimates of $g_c$ to infinite systems. 1) Y. Nakamura and N. Hatano, in preparation.\\ 2) K. Okunishi, Y. Akutsu, N. Akutsu and T. Yamamoto, Phys. Rev. B 64 (2001) 104432.\\ 3) Y. Nakamura and N. Hatano, Physica B 378-380 (2006) 292; J. Phys. Soc. Jpn. 75 (2006) 114001.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Nakamura, Y.N. and Hatano, N.H.}, biburl = {https://www.bibsonomy.org/bibtex/2db2e36194138e295ff621ec3835b2599/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {193fcb6112a25ee37b415705ebe6d357}, intrahash = {db2e36194138e295ff621ec3835b2599}, keywords = {correlation dispersion hubbard length model relation statphys23 topic-8 xxz}, month = {9-13 July}, timestamp = {2007-06-20T10:16:21.000+0200}, title = {Non-Hermitian quantum mechanics of strongly correlated systems}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=486}, year = 2007 }