Orthogonal metals: The simplest non-Fermi liquids

We present a fractionalized metallic phase which is indistinguishable from the Fermi liquid in conductivity and thermodynamics, but is sharply distinct in one-electron properties, such as the electron spectral function. We dub this phase the “orthogonal metal.” The orthogonal metal and the transition to it from the Fermi liquid are naturally described using a slave-particle representation wherein the electron is expressed as a product of a fermion and a slave Ising spin. We emphasize that when the slave spins are disordered, the result is not a Mott insulator (as erroneously assumed in the prior literature), but rather the orthogonal metal. We construct prototypical ground-state wave functions for the orthogonal metal by modifying the Jastrow factor of Slater-Jastrow wave functions that describe ordinary Fermi liquids. We further demonstrate that the transition from the Fermi liquid to the orthogonal metal can, in some circumstances, provide a simple example of a continuous destruction of a Fermi surface with a critical Fermi surface appearing right at the critical point. We present exactly soluble models that realize an orthogonal metal phase, and the phase transition to the Fermi liquid. These models thus provide valuable solvable examples for phase transitions associated with the death of a Fermi surface.

Figure 1

One-loop contributions to the four-point function ${\Gamma }^4(p_1,p_2;p_3,p_4)=\langle \Phi \left(p_1\right)\Phi \left(p_2\right){\Phi }^{*}\left(p_3\right){\Phi }^{*}\left(p_4\right)\rangle$ determining the flow of $u$ in the theory (42). A solid dot denotes a $u$ vertex and a hollow dot a $v$ vertex.

Figure 2

One-loop contributions to the four-point function ${\overline{\Gamma }}^4(p_1,p_2,p_3,p_4)=\langle {\Phi }^{*}\left(p_1\right){\Phi }^{*}\left(p_2\right){\Phi }^{*}\left(p_3\right){\Phi }^{*}\left(p_4\right)\rangle$ determining the flow of $v$ in the theory (42). There are a total of six distinct diagrams obtained by permutating the external momenta $p_1,p_2,p_3,p_4$.

Figure 3

RG flow of coupling constants $u$ and $v$ in the theory (42). Solid and dashed red lines mark separatrices and attractor lines, respectively.