Bose metals and insulators on multileg ladders with ring exchange

Abstract

We establish compelling evidence for the existence of new quasi-one-dimensional descendants of the d-wave Bose liquid (DBL), an exotic two-dimensional quantum phase of uncondensed itinerant bosons characterized by surfaces of gapless excitations in momentum space [O. I. Motrunich and M. P. A. Fisher, Phys. Rev. B 75, 235116 (2007)]. In particular, motivated by a strong-coupling analysis of the gauge theory for the DBL, we study a model of hard-core bosons moving on the N -leg square ladder with frustrating four-site ring exchange. Here, we focus on four-and threeleg systems where we have identified two novel phases: a compressible gapless Bose metal on the four-leg ladder and an incompressible gapless Mott insulator on the three-leg ladder. The former is conducting along the ladder and has five gapless modes, one more than the number of legs. This represents a significant step forward in establishing the potential stability of the DBL in two dimensions. The latter, on the other hand, is a fundamentally quasi-one-dimensional phase that is insulating along the ladder but has two gapless modes and incommensurate power law transverse density-density correlations. While we have already presented results on this latter phase elsewhere [M. S. Block et al., Phys. Rev. Lett. 106, 046402 (2011)], we will expand upon those results in this work. In both cases, we can understand the nature of the phase using slave-particle-inspired variational wave functions consisting of a product of two distinct Slater determinants, the properties of which compare impressively well to a density matrix renormalization group solution of the model Hamiltonian. Stability arguments are made in favor of both quantum phases by accessing the universal low-energy physics with a bosonization analysis of the appropriate quasi-1D gauge theory. We will briefly discuss the potential relevance of these findings to high-temperature superconductors, cold atomic gases, and frustrated quantum magnets.

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

“…However, accessing such a "Bose metal" phase has proven extremely difficult over the years. In recent work, [21][22][23][24] we have indeed succeeded in realizing a concrete, genuine Bose metal phase, which we named the "d-wave Bose liquid" or, equivalently, "d- are fermionic slave particles ("partons") with anisotropic hopping patterns: d 1 (d 2 ) is chosen to hop preferentially in thex (ŷ) direction. The resulting bosonic phase is a conducting, yet uncondensed, quantum fluid, which is precisely the phase into which we place the charge sector of the d-metal.…”

“…38 Also, recently developed tensor network state methods 39 are as of yet unable to handle critical 2D states with a singular surface (e.g., the Fermi liquid and the d-metal) due to the anomalously large amount of spatial entanglement present. 40 We thus follow the heretofore successful [22][23][24]41,42 approach of accessing such phases by studying their quasi-1D descendants on ladder geometries, relying heavily on large-scale DMRG calculations. In fact, we have already established [22][23][24] that for two, three, and four legs, the DBM phase itself is the stable ground state of a boson ring-exchange model analogous to Eq.…”

“…One of the main purposes of Ref. 24 was to establish stability of the d-wave Bose metal, the main ingredient of the d-metal, on three-and four-leg ladders, and this was indeed achieved. Therefore, we do not envision any obvious conceptual obstacles in the way of realizing a similar result for the d-metal; however, we do anticipate that going to more legs will be very challenging numerically due to the large amount of spatial entanglement present.…”

“…However, accessing such a "Bose metal" phase has proven extremely difficult over the years. In recent work, [21][22][23][24] we have indeed succeeded in realizing a concrete, genuine Bose metal phase, which we named the "d-wave Bose liquid" or, equivalently, "d-wave Bose metal" (DBM). The DBM is central to our construction of the d-wave metal.…”

Ordering and criticality in an underscreened Kondo chain

“…Eqs. (16)- (27)]. These singularities can be identified with the singularities present in DMRG QS phase.…”