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SUMMARY:Circuit complexity and 2D bosonisation
DTSTART;VALUE=DATE-TIME:20191212T133000Z
DTEND;VALUE=DATE-TIME:20191212T143000Z
DTSTAMP;VALUE=DATE-TIME:20200219T180948Z
UID:indico-event-20759@agenda.infn.it
DESCRIPTION:We consider the circuit complexity of free bosons\, or equival
ently free fermions\, in 1+1 dimensions. Motivated by the results of [arXi
v:1707.08570] and [arXiv:1803.10638\, arXiv:1801.07620] who found differen
t behavior in the complexity of free bosons and fermions\, in any dimensio
n\, we consider the 1+1 dimensional case where\, thanks to the bosonisatio
n equivalence\, we can consider the same state from both the bosonic and t
he fermionic perspectives. In this way the discrepancy can be attributed t
o a different choice of the set of gates allowed in the circuit. We study
the effect in two classes of states: i) bosonic-coherent / fermionic-gauss
ian states\; ii) states that are both bosonic- and fermionic-gaussian. We
consider the complexity relative to the ground state. In the first class\,
the different results can be reconciled admitting a mode-dependent cost f
unction in one of the descriptions. The differences in the second class ar
e more important\, in terms of the cutoff-dependence and the overall behav
ior of the complexity. The talk will be based on the work arXiv:1904.03003
.\n \n\nhttps://agenda.infn.it/event/20759/
LOCATION:GGI Arcetri Room B
URL:https://agenda.infn.it/event/20759/
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