Abstract
We study a recently proposed quantum dimer model for the pseudogap metal state of the cuprates. The model contains bosonic dimers, representing a spin-singlet valence bond between a pair of electrons, and fermionic dimers, representing a quasiparticle with spin-$1/2$ and charge $+e$. By density matrix renormalization group calculations on a long but finite cylinder, we obtain the ground-state density distribution of the fermionic dimers for a number of different total densities. From the Friedel oscillations at open boundaries, we deduce that the Fermi surface consists of small hole pockets near $(\pi/2, \pi/2)$, and this feature persists up to a doping density of $1/16$. We also compute the entanglement entropy and find that it closely matches the sum of the entanglement entropies of a critical boson and a low density of free fermions. Our results support the existence of a fractionalized Fermi liquid in this model.
Highlights
We study a recently proposed quantum dimer model for the pseudogap metal state of the cuprates
The model of Ref. 1 was designed to yield a Fermi liquid (FL)* state with a Fermi surface of size p using ingredients that are appropriate for a single-band model of cuprate physics
The confinement length scale is large near the Rokhsar and Kivelson (RK) point and at small fermion density, and a spin-liquid U(1)-FL* state should be effectively realized when the confinement scale is larger than the system size
Summary
A recent paper [1] has proposed a simple quantum dimer model for the pseudogap metal state of the hole-doped cuprates. The confinement length scale is large near the RK point and at small fermion density, and a spin-liquid U(1)-FL* state should be effectively realized when the confinement scale is larger than the system size We study such a regime in the present paper, and for our system sizes, our results are consistent with deconfinement. The single fermion study in Ref. 1 suggests the different hopping parameters change the dispersion of the fermionic dimer: the Fermi surface consists of four hole pockets near (±π/2, ±π/2) in the former parameter regime, and a single Fermi surface centered at (0, 0) in the latter We will confirm this behavior in our DMRG calculation below, while studying a multiple fermion system. We kept up to ∼ 600 states to keep the truncation error per step to be ∼ 10−8
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