We calculate the Drude weight in the superfluid (SF) and supersolid (SS) phases of the hard-core boson (HCB) model on a square lattice 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 ${T}_{\mathrm{KT}}$ . The Drude weight, though is equal to the stiffness below ${T}_{\mathrm{KT}}$ , surprisingly, stays finite even for a range of temperatures above ${T}_{\mathrm{KT}}$ indicating the nondissipative 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 via a second-order phase transition at ${T}_{c}$ , the Drude weight goes to zero at ${T}_{c}$ , as expected. We also calculated the Drude weight in a two-dimensional SS phase, where the charge density wave (CDW) order coexists with superfluidity. For the SS phase we studied, superfluidity is lost via a Kosterlitz-Thouless transition at ${T}_{\mathrm{KT}}$ and the transition temperature for the CDW order is larger than ${T}_{\mathrm{KT}}$ . In striped SS phase where the CDW order breaks the rotational symmetry of the lattice, the system behaves like an ideal conductor for a range of temperatures above ${T}_{\mathrm{KT}}$ along the lattice direction parallel to the stripes, while along the direction perpendicular to the stripes it behaves like an insulator for all $T>{T}_{\mathrm{KT}}$ . In contrast to this, in the star-SS phase, the Drude weight along both lattice directions goes to zero along with the superfluid stiffness and for $T>{T}_{\mathrm{KT}}$ we have the finite temperature phase of a CDW insulator.We calculate the Drude weight in the superfluid (SF) and supersolid (SS) phases of the hard-core boson (HCB) model on a square lattice 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 ${T}_{\mathrm{KT}}$. The Drude weight, though is equal to the stiffness below ${T}_{\mathrm{KT}}$, surprisingly, stays finite even for a range of temperatures above ${T}_{\mathrm{KT}}$ indicating the nondissipative 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 via a second-order phase transition at ${T}_{c}$, the Drude weight goes to zero at ${T}_{c}$, as expected. We also calculated the Drude weight in a two-dimensional SS phase, where the charge density wave (CDW) order coexists with superfluidity. For the SS phase we studied, superfluidity is lost via a Kosterlitz-Thouless transition at ${T}_{\mathrm{KT}}$ and the transition temperature for the CDW order is larger than ${T}_{\mathrm{KT}}$. In striped SS phase where the CDW order breaks the rotational symmetry of the lattice, the system behaves like an ideal conductor for a range of temperatures above ${T}_{\mathrm{KT}}$ along the lattice direction parallel to the stripes, while along the direction perpendicular to the stripes it behaves like an insulator for all $T>{T}_{\mathrm{KT}}$. In contrast to this, in the star-SS phase, the Drude weight along both lattice directions goes to zero along with the superfluid stiffness and for $T>{T}_{\mathrm{KT}}$ we have the finite temperature phase of a CDW insulator.

arXiv:1602.03687Physical review. B./Physical review. BOct 12, 20161 citation

{T}_{\mathrm{KT}}

. The Drude weight, though is equal to the stiffness below

{T}_{\mathrm{KT}}

, surprisingly, stays finite even for a range of temperatures above

{T}_{\mathrm{KT}}

indicating the nondissipative 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 via a second-order phase transition at

{T}_{c}

, the Drude weight goes to zero at

{T}_{c}

, as expected. We also calculated the Drude weight in a two-dimensional SS phase, where the charge density wave (CDW) order coexists with superfluidity. For the SS phase we studied, superfluidity is lost via a Kosterlitz-Thouless transition at

{T}_{\mathrm{KT}}

and the transition temperature for the CDW order is larger than

{T}_{\mathrm{KT}}

. In striped SS phase where the CDW order breaks the rotational symmetry of the lattice, the system behaves like an ideal conductor for a range of temperatures above

{T}_{\mathrm{KT}}

along the lattice direction parallel to the stripes, while along the direction perpendicular to the stripes it behaves like an insulator for all

T>{T}_{\mathrm{KT}}

. In contrast to this, in the star-SS phase, the Drude weight along both lattice directions goes to zero along with the superfluid stiffness and for

T>{T}_{\mathrm{KT}}

we have the finite temperature phase of a CDW insulator.