Abstract
The antiferromagnetic spin-$1/2$ Heisenberg model on a kagome lattice is one of the most paradigmatic models in the context of spin liquids, yet the precise nature of its ground state is not understood. We use large scale density matrix normalization group simulations (DMRG) on infinitely long cylinders and find indications for the formation of a gapless Dirac spin liquid. First, we use adiabatic flux insertion to demonstrate that the spin gap is much smaller than estimated from previous DMRG simulation. Second, we find that the momentum dependent excitation spectrum, as extracted from the DMRG transfer matrix, exhibits Dirac cones that match those of a $\pi$-flux free fermion model (the parton mean-field ansatz of a $U(1)$ Dirac spin liquid)
Highlights
Even if a gapless quantum spin liquid (QSL) such as the Dirac spin liquid is realized in the two-dimensional bulk limit, the system generally acquires a nonvanishing gap on the cylinder
The observation of a gap in the previous density matrix renormalization group simulations (DMRG) studies of the KAH, which is reproduced in our study, might not rule out a gapless QSL until the gap can be accurately measured for a sequence of “equivalent” geometries (e.g., YC8; YC12; YC16; ...), which is extremely challenging because of the exponential blowup in DMRG bond dimension
We find that the spin gap on the cylinder geometry is much smaller than estimated from previous DMRG simulations
Summary
Understanding the ground state of the antiferromagnetic spin-1=2 Heisenberg model on a kagome lattice (KAH) has proved to be one of the most vexed issues in quantum magnetism [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. Phase by using extensions to the previously implemented algorithms: (i) We provide new insight into the heavily debated spin gap issue of the KAH by computing its dependence on boundary conditions and show that the spin gap from our DMRG simulations is consistent with a gapless QSL (e.g., DSL). (ii) We obtain the momentumresolved spectrum of correlation lengths of the KAH, which is closely related to the excitation spectrum [48] This spectrum shows signatures of Dirac cones at the locations expected for a gapless DSL [3]. We emphasize that these signatures are seen in the same spin-liquid phase that was reported in previous DMRG simulations [8,11], not a different, competing phase.
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