Superconductivity in doped quantum paramagnets has been a subject of long theoretical inquiry. In this work, we report a density matrix renormalization group study of lightly doped $t\text{\ensuremath{-}}J$ models on the finite-width square lattice (doped hole densities $\ensuremath{\delta}=1/12$ and 1/8) with parameters for which previous studies have suggested that the undoped system in 2D is either a quantum spin liquid or a valence bond crystal. Our studies are performed on cylinders with width up to 8. Ground-state correlations are found to be nearly identical for the ``doped quantum spin liquid'' and ``doped valence bond crystal.'' Upon increasing the cylinder widths from 4 to 8, we observed a significant strengthening of the quasi-long-range superconducting correlations and a dramatic suppression of any ``competing'' charge density wave order. Extrapolating from the observed behavior of the width eight cylinders, we speculate that the system has a nodeless $d$ -wave superconducting ground state in the 2D limit.Superconductivity in doped quantum paramagnets has been a subject of long theoretical inquiry. In this work, we report a density matrix renormalization group study of lightly doped $t\text{\ensuremath{-}}J$ models on the finite-width square lattice (doped hole densities $\ensuremath{\delta}=1/12$ and 1/8) with parameters for which previous studies have suggested that the undoped system in 2D is either a quantum spin liquid or a valence bond crystal. Our studies are performed on cylinders with width up to 8. Ground-state correlations are found to be nearly identical for the ``doped quantum spin liquid'' and ``doped valence bond crystal.'' Upon increasing the cylinder widths from 4 to 8, we observed a significant strengthening of the quasi-long-range superconducting correlations and a dramatic suppression of any ``competing'' charge density wave order. Extrapolating from the observed behavior of the width eight cylinders, we speculate that the system has a nodeless $d$-wave superconducting ground state in the 2D limit.

arXiv:2302.11633Physical review. B./Physical review. BAug 4, 202327 citations

Competing orders II: A spin on the dimer model

Leon Balents, Lorenz Bartosch, A. A. Burkov +2 more

We study the phases of doped spin S=1/2 quantum antiferromagnets on the square lattice, as they evolve from paramagnetic Mott insulators with valence bond solid (VBS) order at zero doping, to superconductors at moderate doping. The interplay between density wave/VBS order and superconductivity is efficiently described by the quantum dimer model, which acts as an effective theory for the total spin S=0 sector. We extend the dimer model to include fermionic S=1/2 excitations, and show that its mean-field, static gauge field saddle points have projective symmetries (PSGs) similar to those of `slave' particle U(1) and SU(2) gauge theories. We account for the non-perturbative effects of gauge fluctuations by a duality mapping of the S=0 dimer model. The dual theory of vortices has a PSG identical to that found in a previous paper (L. Balents et al., cond-mat/0408329) by a duality analysis of bosons on the square lattice. The previous theory therefore also describes fluctuations across superconducting, supersolid and Mott insulating phases of the present electronic model. Finally, with the aim of describing neutron scattering experiments, we present a phenomenological model for collective S=1 excitations and their coupling to superflow and density wave fluctuations.We study the phases of doped spin S=1/2 quantum antiferromagnets on the square lattice, as they evolve from paramagnetic Mott insulators with valence bond solid (VBS) order at zero doping, to superconductors at moderate doping. The interplay between density wave/VBS order and superconductivity is efficiently described by the quantum dimer model, which acts as an effective theory for the total spin S=0 sector. We extend the dimer model to include fermionic S=1/2 excitations, and show that its mean-field, static gauge field saddle points have projective symmetries (PSGs) similar to those of `slave' particle U(1) and SU(2) gauge theories. We account for the non-perturbative effects of gauge fluctuations by a duality mapping of the S=0 dimer model. The dual theory of vortices has a PSG identical to that found in a previous paper (L. Balents et al., cond-mat/0408329) by a duality analysis of bosons on the square lattice. The previous theory therefore also describes fluctuations across superconducting, supersolid and Mott insulating phases of the present electronic model. Finally, with the aim of describing neutron scattering experiments, we present a phenomenological model for collective S=1 excitations and their coupling to superflow and density wave fluctuations.

Sep 20, 20040 citations

Putting competing orders in their place near the Mott transition. II. The doped quantum dimer model

Leon Balents, Lorenz Bartosch, A. A. Burkov +2 more

We study the phases of doped spin $S=1∕2$ quantum antiferromagnets on the square lattice as they evolve from paramagnetic Mott insulators with valence bond solid (VBS) order at doping $\ensuremath{\delta}=0$ to superconductors at moderate $\ensuremath{\delta}$. The interplay between density-wave and VBS order and superconductivity is efficiently described by the quantum dimer model, which acts as an effective theory for the total spin $S=0$ sector. We extend the dimer model to include fermionic $S=1∕2$ excitations and show that its mean-field, static gauge-field saddle points have projective symmetries (PSG's) similar to those of ``slave''-particle U(1) and SU(2) gauge theories. We account for the nonperturbative effects of gauge fluctuations by a duality mapping of the $S=0$ dimer model. The dual theory of vortices has a PSG identical to that found in a previous paper [L. Balents et al., preceding paper, Phys. Rev. B 71, 144508 (2005)] by a duality analysis of bosons on the square lattice. The previous theory therefore also describes fluctuations across superconducting, supersolid, and Mott insulating phases of the present electronic model. Finally, with the aim of describing neutron scattering experiments, we present a phenomenological model for collective $S=1$ excitations and their coupling to superflow and density-wave fluctuations.We study the phases of doped spin $S=1∕2$ quantum antiferromagnets on the square lattice as they evolve from paramagnetic Mott insulators with valence bond solid (VBS) order at doping $\ensuremath{\delta}=0$ to superconductors at moderate $\ensuremath{\delta}$. The interplay between density-wave and VBS order and superconductivity is efficiently described by the quantum dimer model, which acts as an effective theory for the total spin $S=0$ sector. We extend the dimer model to include fermionic $S=1∕2$ excitations and show that its mean-field, static gauge-field saddle points have projective symmetries (PSG's) similar to those of ``slave''-particle U(1) and SU(2) gauge theories. We account for the nonperturbative effects of gauge fluctuations by a duality mapping of the $S=0$ dimer model. The dual theory of vortices has a PSG identical to that found in a previous paper [L. Balents et al., preceding paper, Phys. Rev. B 71, 144508 (2005)] by a duality analysis of bosons on the square lattice. The previous theory therefore also describes fluctuations across superconducting, supersolid, and Mott insulating phases of the present electronic model. Finally, with the aim of describing neutron scattering experiments, we present a phenomenological model for collective $S=1$ excitations and their coupling to superflow and density-wave fluctuations.

arXiv:cond-mat/0409470Physical Review BApr 19, 200550 citations

Exact theory for superconductivity in a doped Mott insulator

Philip Phillips, Luke Yeo, Edwin W. Huang

arXiv:1912.01008Nature PhysicsJul 27, 2020107 citations

d

-wave superconducting ground state in the 2D limit.

We study the phases of doped spin

S=1∕2

quantum antiferromagnets on the square lattice as they evolve from paramagnetic Mott insulators with valence bond solid (VBS) order at doping $\ensuremath{\delta}=0$ to superconductors at moderate $\ensuremath{\delta}$. The interplay between density-wave and VBS order and superconductivity is efficiently described by the quantum dimer model, which acts as an effective theory for the total spin

S=0

sector. We extend the dimer model to include fermionic

S=1∕2

excitations and show that its mean-field, static gauge-field saddle points have projective symmetries (PSG's) similar to those of ``slave''-particle U(1) and SU(2) gauge theories. We account for the nonperturbative effects of gauge fluctuations by a duality mapping of the

S=0

dimer model. The dual theory of vortices has a PSG identical to that found in a previous paper [L. Balents et al., preceding paper, Phys. Rev. B 71, 144508 (2005)] by a duality analysis of bosons on the square lattice. The previous theory therefore also describes fluctuations across superconducting, supersolid, and Mott insulating phases of the present electronic model. Finally, with the aim of describing neutron scattering experiments, we present a phenomenological model for collective

S=1

excitations and their coupling to superflow and density-wave fluctuations.