Localization properties of random-mass Dirac fermions for a realization of mass disorder, commonly referred to as the Cho-Fisher model, are studied on the D-class chiral network. We show that a simple renormalization group (RG) description captures accurately a rich phase diagram: thermal metal and two insulators with quantized σ(xy), as well as transitions (including critical exponents) between them. Our main finding is that, even with small transmission of nodes, the RG block exhibits a sizable portion of perfect resonances. Delocalization occurs by proliferation of these resonances to larger scales. Evolution of the thermal conductance distribution towards a metallic fixed point is synchronized with evolution of signs of transmission coefficients, so that delocalization is accompanied with sign percolation.
Thermal tensor networks constitute an efficient and versatile representation for quantum lattice models at finite temperatures. By Trotter-Suzuki decomposition, one obtains a
D+1 dimensional TTN for the
D-dimensional quantum system and then employs efficient renormalizaton group (RG) contractions to obtain the thermodynamic properties with high precision. The linearized tensor renormalization group (LTRG) method, which can be used to contract TTN efficiently and calculate the thermodynamics, is briefly reviewed and then generalized to a bilayer form. We dub this bilayer algorithm as LTRG++ and explore its performance in both finite- and infinite-size systems, finding the numerical accuracy significantly improved compared to single-layer algorithm. Moreover, we show that the LTRG++ algorithm in an infinite-size system is in essence equivalent to transfer-matrix renormalization group method, while reformulated in a tensor network language. As an application of LTRG++, we simulate an extended fermionic Hubbard model numerically, where the phase separation phenomenon, ground-state phase diagram, as well as quantum criticality-enhanced magnetocaloric effects, are investigated.
We investigate how the strong coupling of a superconductor to thermal bosons can enhance its superconducting critical temperature. To tackle this problem, we use a renormalization group approach that allows us to describe the competition between density fluctuations and the build-up of boson-induced attraction between fermions. Capturing the mutual influence of bosonic and fermionic sectors, the self-consistent renormalization group framework predicts a robust increase of the critical temperature across a wide range of interactions. We find a nontrivial dependence of the critical temperature on the boson mass and we establish a phase diagram for enhanced superconductivity driven by bosons being either in the condensed or thermal state. We outline possible experimental realizations in cold atomic systems and discuss implementations using electron-exciton mixtures in van der Waals material heterostructures.