Fixed points and critical temperature near quantum critical points in $d$ -wave cuprate superconductorsFixed points and critical temperature near quantum critical points in $d$-wave cuprate superconductors

Qi-Qi Yue, Yi-sheng Fu, Jing Wang

We study the critical behavior driven by potential quantum critical points (QCPs) termed as $τ_{0,x,y,z}$ -Type QCPs in the $d$ -wave cuprate superconductors. Within the framework of the renormalization group approach, we construct the coupled flow equations of all interaction parameters and obtain several unique properties. On one hand, the interaction parameters flow toward several fixed points (FPs) at certain critical energy scales. We identify two different types of FPs designated at the clean limit. FP-I is characterized by the divergence of the quadratic parameter and exhibits robustness against variations in interaction parameters. In contrast, FP-II is dominated by the cubic and quartic interaction parameters, and it is sensitive to initial conditions, leading to five subclasses. Besides, we find that disorder scattering can influence fermion velocities and critical energy scales, and even destabilize certain FPs around the $τ_{x,z}$ -QCPs, driving the system toward a preempted disorder-induced FP. On the other hand, we find that quantum fluctuations play a critical role in shaping the critical temperature ( $T_c$ ) as the system approaches these QCPs. Near the $τ_x$ -QCP, $T_c$ is considerably suppressed for both FP-I and FP-II. In contrast, near the $τ_0$ -QCP, $T_c$ undergoes a substantial decrease for FP-I but only a slight decrease for FP-II. Conversely, $T_c$ exhibits an increasing trend near the $τ_y$ -QCP, with a pronounced peak at $v_{Δ0}/v_{F0} \sim 0.25$ . However, numerical analysis suggests that the $τ_z$ -QCP is unlikely to be physically realizable. Additionally, we realize that $T_c$ can also be modified by the emergence of disorder-induced FPs in the vicinity of the $τ_x$ -QCP. These findings would provide valuable insights into the critical low-energy properties of $d$ -wave cuprate superconductors and related materials.We study the critical behavior driven by potential quantum critical points (QCPs) termed as $τ_{0,x,y,z}$-Type QCPs in the $d$-wave cuprate superconductors. Within the framework of the renormalization group approach, we construct the coupled flow equations of all interaction parameters and obtain several unique properties. On one hand, the interaction parameters flow toward several fixed points (FPs) at certain critical energy scales. We identify two different types of FPs designated at the clean limit. FP-I is characterized by the divergence of the quadratic parameter and exhibits robustness against variations in interaction parameters. In contrast, FP-II is dominated by the cubic and quartic interaction parameters, and it is sensitive to initial conditions, leading to five subclasses. Besides, we find that disorder scattering can influence fermion velocities and critical energy scales, and even destabilize certain FPs around the $τ_{x,z}$-QCPs, driving the system toward a preempted disorder-induced FP. On the other hand, we find that quantum fluctuations play a critical role in shaping the critical temperature ($T_c$) as the system approaches these QCPs. Near the $τ_x$-QCP, $T_c$ is considerably suppressed for both FP-I and FP-II. In contrast, near the $τ_0$-QCP, $T_c$ undergoes a substantial decrease for FP-I but only a slight decrease for FP-II. Conversely, $T_c$ exhibits an increasing trend near the $τ_y$-QCP, with a pronounced peak at $v_{Δ0}/v_{F0} \sim 0.25$. However, numerical analysis suggests that the $τ_z$-QCP is unlikely to be physically realizable. Additionally, we realize that $T_c$ can also be modified by the emergence of disorder-induced FPs in the vicinity of the $τ_x$-QCP. These findings would provide valuable insights into the critical low-energy properties of $d$-wave cuprate superconductors and related materials.

arXiv:2503.20347Mar 26, 20250 citations

Weak disorder effects on criticality in quantum systems

Gaetano Busiello, L. De Cesare, Ileana Rabuffo

Jan 1, 19861 citation

Scaling of entanglement entropy at quantum critical points in random spin chains

Prashant Kumar, R. N. Bhatt

We study the scaling properties of entanglement entropy (EE) near the quantum critical points in interacting random antiferromagnetic (AFM) spin chains. Using density-matrix renormalization group, we compute the half-chain EE near the topological phase transition between the Haldane and random singlet phases in a disordered spin-1 chain. It is found to diverge logarithmically in system size with an effective central charge ${c}_{\mathrm{eff}}=1.17(4)$ at the quantum critical point (QCP). Moreover, a scaling analysis of EE yields the correlation length exponent $\ensuremath{\nu}=2.28(5)$. Our unbiased calculation establishes that the QCP is in the universality class of the infinite-randomness fixed point predicted by previous studies based on the strong disorder renormalization group technique. However, in the disordered spin-1/2 Majumdar-Ghosh chain, where a valence bond solid phase is unstable to disorder, the crossover length exponent obtained from a scaling analysis of EE disagrees with the expectation based on the Imry-Ma argument. We provide a possible explanation.We study the scaling properties of entanglement entropy (EE) near the quantum critical points in interacting random antiferromagnetic (AFM) spin chains. Using density-matrix renormalization group, we compute the half-chain EE near the topological phase transition between the Haldane and random singlet phases in a disordered spin-1 chain. It is found to diverge logarithmically in system size with an effective central charge ${c}_{\mathrm{eff}}=1.17(4)$ at the quantum critical point (QCP). Moreover, a scaling analysis of EE yields the correlation length exponent $\ensuremath{\nu}=2.28(5)$. Our unbiased calculation establishes that the QCP is in the universality class of the infinite-randomness fixed point predicted by previous studies based on the strong disorder renormalization group technique. However, in the disordered spin-1/2 Majumdar-Ghosh chain, where a valence bond solid phase is unstable to disorder, the crossover length exponent obtained from a scaling analysis of EE disagrees with the expectation based on the Imry-Ma argument. We provide a possible explanation.

arXiv:2307.00062Physical review. B./Physical review. BDec 15, 20232 citations

Quantum Critical Behavior in the Asymptotic Limit of High Disorder

Brian C. Sales

Bulletin of the American Physical SocietyMar 9, 20180 citations

Fixed points and critical temperature near quantum critical points in

d

-wave cuprate superconductors

We study the critical behavior driven by potential quantum critical points (QCPs) termed as

τ_{0,x,y,z}

-Type QCPs in the

d

-wave cuprate superconductors. Within the framework of the renormalization group approach, we construct the coupled flow equations of all interaction parameters and obtain several unique properties. On one hand, the interaction parameters flow toward several fixed points (FPs) at certain critical energy scales. We identify two different types of FPs designated at the clean limit. FP-I is characterized by the divergence of the quadratic parameter and exhibits robustness against variations in interaction parameters. In contrast, FP-II is dominated by the cubic and quartic interaction parameters, and it is sensitive to initial conditions, leading to five subclasses. Besides, we find that disorder scattering can influence fermion velocities and critical energy scales, and even destabilize certain FPs around the

τ_{x,z}

-QCPs, driving the system toward a preempted disorder-induced FP. On the other hand, we find that quantum fluctuations play a critical role in shaping the critical temperature (

T_c

) as the system approaches these QCPs. Near the

τ_x

-QCP,

T_c

is considerably suppressed for both FP-I and FP-II. In contrast, near the

τ_0

-QCP,

T_c

undergoes a substantial decrease for FP-I but only a slight decrease for FP-II. Conversely,

T_c

exhibits an increasing trend near the

τ_y

-QCP, with a pronounced peak at

v_{Δ0}/v_{F0} \sim 0.25

. However, numerical analysis suggests that the

τ_z

-QCP is unlikely to be physically realizable. Additionally, we realize that

T_c

can also be modified by the emergence of disorder-induced FPs in the vicinity of the

τ_x

-QCP. These findings would provide valuable insights into the critical low-energy properties of

d

-wave cuprate superconductors and related materials.

{c}_{\mathrm{eff}}=1.17(4)

at the quantum critical point (QCP). Moreover, a scaling analysis of EE yields the correlation length exponent $\ensuremath{\nu}=2.28(5)$. Our unbiased calculation establishes that the QCP is in the universality class of the infinite-randomness fixed point predicted by previous studies based on the strong disorder renormalization group technique. However, in the disordered spin-1/2 Majumdar-Ghosh chain, where a valence bond solid phase is unstable to disorder, the crossover length exponent obtained from a scaling analysis of EE disagrees with the expectation based on the Imry-Ma argument. We provide a possible explanation.