|
| related topics |
| {energy, state, states} |
| {information, entropy, channel} |
| {equation, function, exp} |
| {entanglement, phys, rev} |
| {operator, operators, space} |
| {let, theorem, proof} |
| {cos, sin, state} |
| {energy, gaussian, time} |
| {temperature, thermal, energy} |
|
Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
B. -Q. Jin, V. E. Korepin
abstract: We consider one-dimensional quantum spin chain, which is called XX model, XX0
model or isotropic XY model in a transverse magnetic field. We study the model
on the infinite lattice at zero temperature. We are interested in the entropy
of a subsystem [a block of L neighboring spins]. It describes entanglement of
the block with the rest of the ground state.
G. Vidal, J.I. Latorre, E. Rico, and A. Kitaev showed that for large blocks
the entropy scales logarithmically. We prove the logarithmic formula for the
leading term and calculate the next term.
We discovered that the dependence on the magnetic field interacting with spins
is very simple: the magnetic field effectively reduce the size of the
subsystem.
We also calculate entropy of a subsystem of a small size. We also evaluated
Renyi and Tsallis entropies of the subsystem. We represented the entropy in
terms of a Toeplitz determinant and calculated the asymptotic analytically.
- oai_identifier:
- oai:arXiv.org:quant-ph/0304108
- categories:
- quant-ph cond-mat.stat-mech math-ph math.MP
- comments:
- LATEX, 17 pages, 1 fig
- doi:
- 10.1023/B:JOSS.0000037230.37166.42
- arxiv_id:
- quant-ph/0304108
- journal_ref:
- Journal of Statistical Physics, vol 116, Nos. 1-4, pages 79-95,
August 2004
- report_no:
- YITP-SB-03-16
- created:
- 2003-04-15
- updated:
- 2003-12-16
Full article ▸
|
|
| related documents |
| 0612175v1 |
| 0612039v1 |
| 0505205v2 |
| 9808041v1 |
| 0512135v1 |
| 9802024v2 |
| 0603123v3 |
| 0606216v2 |
| 0507266v1 |
| 0603042v1 |
| 0209119v1 |
| 0401150v1 |
| 0208144v2 |
| 9605001v1 |
| 0312030v1 |
| 0509023v3 |
| 0508172v2 |
| 0008048v1 |
| 0204139v1 |
| 0203024v1 |
| 0506022v2 |
| 9904064v1 |
| 0702078v2 |
| 0508185v2 |
| 0506156v2 |
|