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Register a new userProposal for measuring the finite-temperature Drude weight of integrable systems
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Integrable models such as the spin-1/2 Heisenberg chain, the Lieb-Liniger or the one-dimensional Hubbard model are known to avoid thermalization, which was also demonstrated in several quantum-quench experiments. Another dramatic consequence of integrability is the zero-frequency anomaly in transport coefficients, which results in ballistic finite-temperature transport, despite the presence of strong interactions. While this aspect of nonergodic dynamics has been known for a long time, there has so far not been any unambiguous experimental realization thereof. We make a concrete proposal for the observation ballistic transport via local quantum quench experiments in fermionic quantum-gas microscopes. Such an experiment would also unveil the coexistence of ballistic and diffusive transport channels in one and the same system and provide a means of measuring finite-temperature Drude weights. The connection between local quenches and linear-response functions is established via time-dependent Einstein relations.
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We calculate the Drude weight in the superfluid (SF) and the supersolid (SS) phases of hard core boson (HCB) model using stochastic series expansion (SSE). We demonstrate from our numerical calculations that the normal phase of HCBs in two dimensions can be an ideal conductor with dissipationless transport. In two dimensions, when the ground state is a SF, the superfluid stiffness drops to zero with a Kosterlitz-Thouless type transition at $T_{KT}$. The Drude weight, though is equal to the stiffness below $T_{KT}$, surprisingly stays finite even for temperatures above $T_{KT}$ indicating the non-dissipative transport in the normal state of this system. In contrast to this in a three dimensional SF phase, where the superfluid stiffness goes to zero continuously with a second order phase transition at $T_c$, Drude weight also goes to zero at $T_c$ as expected. We also calculated the Drude weight in a 2D SS phase, where the charge density wave (CDW) order coexists with superfluidity. For the SS phase we studied, superfluidity is lost via Kosterlitz-Thouless transition at $T_{KT}$ and the transition temperature for the CDW order is larger than $T_{KT}$. In striped SS phase where the CDW order breaks the rotational symmetry of the lattice, for $T > T_{KT}$, the system behaves like an ideal conductor along one of the lattice direction while along the other direction it behaves like an insulator. In contrast to this, in star-SS phase, Drude weight along both the lattice directions goes to zero along with the superfluid stiffness and for $T > T_{KT}$ we have a finite temperature phase of a CDW insulator.
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