Shannon and entanglement entropies of one- and two-dimensional critical wave functions TeX Export

@article{citeulike:4775232, abstract = {We study the Shannon entropy of the probability distribution resulting from the ground-state wave function of a one-dimensional quantum model. This entropy is related to the entanglement entropy of a Rokhsar-Kivelson-type wave function built from the corresponding two-dimensional classical model. In both critical and massive cases, we observe that it is composed of an extensive part proportional to the length of the system and a subleading universal constant \$S\_0\$. In \$c=1\$ critical systems (Tomonaga-Luttinger liquids), we find that \$S\_0\$ is a simple function of the boson compactification radius. This finding is based on a field-theoretical analysis of the Dyson-Gaudin gas related to dimer and Calogero-Sutherland models. We also performed numerical demonstrations in the dimer models and the spin-1/2 XXZ chain. In a massive (crystal) phase, \$S\_0\$ is related to the ground-state degeneracy. We also examine this entropy in the Ising chain in a transverse field as an example showing a \$c=1/2\$ critical point.}, archivePrefix = {arXiv}, author = {St\&\#xe9;phan, Jean-Marie and Furukawa, Shunsuke and Misguich, Gr\&\#xe9;goire and Pasquier, Vincent}, citeulike-article-id = {4775232}, citeulike-linkout-0 = {http://arxiv.org/abs/0906.1153}, citeulike-linkout-1 = {http://arxiv.org/pdf/0906.1153}, eprint = {0906.1153}, keywords = {enganglement-entropy, entropy, quantum-entropy}, month = {Jun}, posted-at = {2009-07-02 21:26:12}, priority = {2}, title = {Shannon and entanglement entropies of one- and two-dimensional critical wave functions}, url = {http://arxiv.org/abs/0906.1153}, year = {2009} }

TY - JOUR ID - citeulike:4775232 L3 - citeulike-article-id:4775232 N2 - We study the Shannon entropy of the probability distribution resulting from the ground-state wave function of a one-dimensional quantum model. This entropy is related to the entanglement entropy of a Rokhsar-Kivelson-type wave function built from the corresponding two-dimensional classical model. In both critical and massive cases, we observe that it is composed of an extensive part proportional to the length of the system and a subleading universal constant $S_0$. In $c=1$ critical systems (Tomonaga-Luttinger liquids), we find that $S_0$ is a simple function of the boson compactification radius. This finding is based on a field-theoretical analysis of the Dyson-Gaudin gas related to dimer and Calogero-Sutherland models. We also performed numerical demonstrations in the dimer models and the spin-1/2 XXZ chain. In a massive (crystal) phase, $S_0$ is related to the ground-state degeneracy. We also examine this entropy in the Ising chain in a transverse field as an example showing a $c=1/2$ critical point. TI - Shannon and entanglement entropies of one- and two-dimensional critical wave functions KW - enganglement-entropy KW - entropy KW - quantum-entropy AU - Stéphan, Jean-Marie AU - Furukawa, Shunsuke AU - Misguich, Grégoire AU - Pasquier, Vincent PY - 2009/Jun/05/ UR - http://arxiv.org/abs/0906.1153 ER -