Theory of edge induced quantum critical phenomena in strongly correlated system

Dangling edge spins of two-dimensional quantum critical antiferromagnets display strongly enhanced spin correlations with scaling dimensions that fall outside of the classical theory of surface critical phenomena. We provide large-scale quantum Monte Carlo results for both spin-correlation and bond-correlation functions for the case of the columnar dimer model in particular. Unlike the spin correlations, we find the bond correlations to differ starkly between the spin-1/2 and spin-1 case. Furthermore, we compare the corresponding scaling dimensions to recent theoretical predictions. These predictions are, in part, supported by our numerical data, but cannot explain our findings completely. Our results thus put further constraints on completing the understanding of dangling edge correlations, as well as surface phenomena in strongly correlated quantum systems in general.Dangling edge spins of two-dimensional quantum critical antiferromagnets display strongly enhanced spin correlations with scaling dimensions that fall outside of the classical theory of surface critical phenomena. We provide large-scale quantum Monte Carlo results for both spin-correlation and bond-correlation functions for the case of the columnar dimer model in particular. Unlike the spin correlations, we find the bond correlations to differ starkly between the spin-1/2 and spin-1 case. Furthermore, we compare the corresponding scaling dimensions to recent theoretical predictions. These predictions are, in part, supported by our numerical data, but cannot explain our findings completely. Our results thus put further constraints on completing the understanding of dangling edge correlations, as well as surface phenomena in strongly correlated quantum systems in general.

arXiv:2010.15691Physical review. B./Physical review. BJan 13, 202117 citations

Scaling Theory of Quantum Critical Phenomena

World Scientific lecture notes in physicsJan 1, 20010 citations

Emergence of strongly correlated electronic states driven by the Andreev bound state in d -wave superconductors

Shun Matsubara, Hiroshi Kontani

As the surface Andreev bound state (ABS) forms at the open (1,1) edge of a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductor, the local density of states increases. Therefore, a strong electron correlation and drastic phenomena may occur. However, a theoretical study on the effects of the ABS on the electron correlation has not been performed yet. To understand these effects, we study the large-cluster Hubbard model with an open (1,1) edge in the presence of a bulk $d$ -wave gap. We calculate the site-dependent spin susceptibility by performing the random-phase approximation and modified fluctuation-exchange approximation in real space. We find that near the (1,1) edge, drastic ferromagnetic (FM) fluctuations occur owing to the ABS. In addition, as the temperature decreases, the system rapidly approaches a magnetic-order phase slightly below the transition temperature of the bulk $d$ -wave superconductivity (SC). In this case, the FM fluctuations are expected to induce interesting phenomena such as edge-induced triplet SC and quantum critical phenomena.As the surface Andreev bound state (ABS) forms at the open (1,1) edge of a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductor, the local density of states increases. Therefore, a strong electron correlation and drastic phenomena may occur. However, a theoretical study on the effects of the ABS on the electron correlation has not been performed yet. To understand these effects, we study the large-cluster Hubbard model with an open (1,1) edge in the presence of a bulk $d$-wave gap. We calculate the site-dependent spin susceptibility by performing the random-phase approximation and modified fluctuation-exchange approximation in real space. We find that near the (1,1) edge, drastic ferromagnetic (FM) fluctuations occur owing to the ABS. In addition, as the temperature decreases, the system rapidly approaches a magnetic-order phase slightly below the transition temperature of the bulk $d$-wave superconductivity (SC). In this case, the FM fluctuations are expected to induce interesting phenomena such as edge-induced triplet SC and quantum critical phenomena.

arXiv:1910.08727Physical review. B./Physical review. BFeb 12, 20209 citations

Edge-induced Strongly Correlated Electronic States in Two-dimensional Hubbard Model: Enhancement of Magnetic Correlations and Self-energy Effects

Shun Matsubara, Youichi Yamakawa, Hiroshi Kontani

To understand nontrivial edge electronic states in strongly-correlated metals such as cuprate superconductors, we study the two-dimensional Hubbard models with open edge boundary. The position-dependences of the spin susceptibility and the self-energy are carefully analyzed self-consistently, by using the fluctuation-exchange (FLEX) approximation. It is found that spin susceptibilities are strongly enlarged near the (1,1) open edge when the system is near the half-filling. The enhancement is large even if the negative feedback from the self-energy is considered in the FLEX approximation. The present study predicts the emergence of nontrivial spin-fluctuation-driven phenomena near the edge, like the quantum criticality, edge superconductivity, and the bond-density-wave order.To understand nontrivial edge electronic states in strongly-correlated metals such as cuprate superconductors, we study the two-dimensional Hubbard models with open edge boundary. The position-dependences of the spin susceptibility and the self-energy are carefully analyzed self-consistently, by using the fluctuation-exchange (FLEX) approximation. It is found that spin susceptibilities are strongly enlarged near the (1,1) open edge when the system is near the half-filling. The enhancement is large even if the negative feedback from the self-energy is considered in the FLEX approximation. The present study predicts the emergence of nontrivial spin-fluctuation-driven phenomena near the edge, like the quantum criticality, edge superconductivity, and the bond-density-wave order.

arXiv:1805.10011Journal of the Physical Society of JapanJun 15, 20184 citations

d

-wave gap. We calculate the site-dependent spin susceptibility by performing the random-phase approximation and modified fluctuation-exchange approximation in real space. We find that near the (1,1) edge, drastic ferromagnetic (FM) fluctuations occur owing to the ABS. In addition, as the temperature decreases, the system rapidly approaches a magnetic-order phase slightly below the transition temperature of the bulk

d

-wave superconductivity (SC). In this case, the FM fluctuations are expected to induce interesting phenomena such as edge-induced triplet SC and quantum critical phenomena.