TY - JOUR
T1 - Non-local order in Mott insulators, duality and Wilson loops
AU - Rath, Steffen Patrick
AU - Simeth, Wolfgang
AU - Endres, Manuel
AU - Zwerger, Wilhelm
N1 - Funding Information:
We acknowledge useful comments by Nigel Cooper and Senthil Todadri. This work has been supported by the DFG Forschergruppe 801 .
PY - 2013/7
Y1 - 2013/7
N2 - It is shown that the Mott insulating and superfluid phases of bosons in an optical lattice may be distinguished by a non-local 'parity order parameter' which is directly accessible via single site resolution imaging. In one dimension, the lattice Bose model is dual to a classical interface roughening problem. We use known exact results from the latter to prove that the parity order parameter exhibits long range order in the Mott insulating phase, consistent with recent experiments by Endres et al. [M.Endres, M.Cheneau, T.Fukuhara, C.Weitenberg, P.Schauß, C.Gross, L.Mazza, M.C.Bañuls, L.Pollet, I.Bloch, etal., Science 334 (2011) 200]. In two spatial dimensions, the parity order parameter can be expressed in terms of an equal time Wilson loop of a non-trivial U (1) gauge theory in 2 + 1 dimensions which exhibits a transition between a Coulomb and a confining phase. The negative logarithm of the parity order parameter obeys a perimeter law in the Mott insulator and is enhanced by a logarithmic factor in the superfluid.
AB - It is shown that the Mott insulating and superfluid phases of bosons in an optical lattice may be distinguished by a non-local 'parity order parameter' which is directly accessible via single site resolution imaging. In one dimension, the lattice Bose model is dual to a classical interface roughening problem. We use known exact results from the latter to prove that the parity order parameter exhibits long range order in the Mott insulating phase, consistent with recent experiments by Endres et al. [M.Endres, M.Cheneau, T.Fukuhara, C.Weitenberg, P.Schauß, C.Gross, L.Mazza, M.C.Bañuls, L.Pollet, I.Bloch, etal., Science 334 (2011) 200]. In two spatial dimensions, the parity order parameter can be expressed in terms of an equal time Wilson loop of a non-trivial U (1) gauge theory in 2 + 1 dimensions which exhibits a transition between a Coulomb and a confining phase. The negative logarithm of the parity order parameter obeys a perimeter law in the Mott insulator and is enhanced by a logarithmic factor in the superfluid.
KW - Duality
KW - Mott insulator
KW - Non-local order
KW - Optical lattice
KW - Wilson loop
UR - http://www.scopus.com/inward/record.url?scp=84877064485&partnerID=8YFLogxK
U2 - 10.1016/j.aop.2013.04.006
DO - 10.1016/j.aop.2013.04.006
M3 - Article
AN - SCOPUS:84877064485
SN - 0003-4916
VL - 334
SP - 256
EP - 271
JO - Annals of Physics
JF - Annals of Physics
ER -