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We propose that the non-equilibrium current measured in the $a-b$ plane of an underdoped cuprate (in either the strange metal or pseudogap regime) in contact with either an overdoped cuprate or a standard Fermi liquid can be used diagnose how different the pseudogap and strange metals are from a Fermi liquid. Naively one expects the strange metal to be more different from a Fermi liquid than is the pseudogap. We compute the expected non-equilibrium transport signal with the three Green functions that are available in the literature: 1) marginal Fermi liquid theory, 2) the phenomenological ansatz for the pseudogap regime and 3) the Wilsonian reduction of the Hubbard model which contains both the strange metal and pseudogap. All three give linear IV curves at low bias voltages. Significant deviations from linearity at higher voltages obtain only in the marginal Fermi liquid approach. The key finding, however, is that IV curves for the strange metal/Fermi liquid contact that exceed that of the pseudogap/Fermi liquid system. If this is borne out experimentally, this implies that the strange metal is less orthogonal to a Fermi liquid than is the pseudogap. Within the Wilsonian reduction of the Hubbard model, this result is explained in terms of a composite-particle picture. Namely, the pseudogap corresponds to a confinement transition of the charge degrees of freedom present in the strange metal. In the strange metal the composite excitations break up and electron quasiparticles scatter off bosons. The bosons here, however, do not arise from phonons but from the charge degrees of freedom responsible for dynamical spectral weight transfer., submitted to PRB

We investigate the instabilities of the Mott-insulating phase of the weakly disordered Bose-Hubbard model within a renormalization group analysis of the replica field theory obtained by a strong-coupling expansion around the atomic limit. We identify a new order parameter and associated correlation length scale that is capable of capturing the transition from a state with zero compressibility, the Mott insulator, to one in which the compressibility is finite, the Bose glass. The order parameter is the relative variance of the disorder-induced mass distribution. In the Mott insulator, the relative variance renormalizes to zero, whereas it diverges in the Bose glass. The divergence of the relative variance signals the breakdown of self-averaging. The length scale governing the breakdown of self-averaging is the distance between rare regions. This length scale is finite in the Bose glass but diverges at the transition to the Mott insulator with an exponent of $\nu=1/D$ for incommensurate fillings. Likewise, the compressibility vanishes with an exponent of $\gamma=4/D-1$ at the transition. At commensurate fillings, the transition is controlled by a different fixed point at which both the disorder and interaction vertices are relevant., Comment: Extended, published version

Two remarkable features emerge from the exact Wilsonian procedure for integrating out the high-energy scale in the Hubbard model. At low energies, the number of excitations that couple minimally to the electromagnetic gauge is less than the conserved charge, thereby implying a breakdown of Fermi liquid theory. In addition, two charge $e$ excitations emerge in the lower band, the standard projected electron and a composite entity (comprised of a hole and a charge $2e$ bosonic field) which give rise to poles and zeros of the single-particle Green function, respectively. The poles generate spectral weight along an arc centered at $(\pi/2,\pi/2)$ while the zeros kill the spectral intensity on the back-side of the arc. The result is the Fermi arc structure intrinsic to cuprate phenomenology. The presence of composite excitations also produces a broad incoherent pseudogap feature at the $(\pi,0)$ region of the Brillouin zone, thereby providing a mechanism for the nodal/anti-nodal dichotomy seen in the cuprates., Comment: 8 pages, 4 figures: Extended version accepted to PRB. Additions include: 1) proof that the (\pi,\pi) solution is a global minimum, 2) extensive discussion of relation to SU(2) gauge theory of t-J model and 3) the meaning of the zero modes given the absence of Luttinger's theorem established in arXiv:1207.4201. New Published version

Hall and optical conductivity experiments on the cuprates indicate that the low-energy fermionic degrees of freedom in a doped Mott insulator posess a component that is dynamcially generated and hence determined by the temperature. We show explicitly how the spectrum in the lower Hubbard band should be partitioned to describe such dynamically generated charge degrees of freedom and corroborate this picture with the results from the exact low-energy theory of the Hubbard model. A consequence of such dynamics is that the Landau one-to-one correspondence between bare electrons and the effective fermionic degrees of freedom at low energies breaks down explicitly. This state of affairs obtains because the total hole number is not conserved as it contains a dynamical contribution. We propose that any experimental probe that couples to the low-energy dynamics of a doped Mott insulator, quantum oscillation experiments included, should be interpreted in terms of the total dynamically generated hole number rather than the bare value., Comment: 6 pages, 2 figures: Published version