Session B02: Quantum and Classical Many-Particle Systems

Understanding unconventional superconductivity through cuprate ladders

Despite more than thirty years of research, even the minimal model required to understand the high critical temperature cuprate superconductors is still under debate. One model system that is well understood and believed by many to be relevant to real cuprates is the single band two-leg ladder. Particles doped into a ladder break rung singlet pairs, leading to an effective attraction and dominant superconducting pairing correlations in the long-range limit. This result appears to explain the superconductivity found in the one known cuprate with a coupled ladder structure, Sr_14-xCa_xCu₂₄O₄₁ (SCCO), where superconductivity is found under simultaneous doping and application of pressure.  Increases in computer power now allow accurate solutions of cuprate ladders within a three-band model including both copper and oxygen atoms. We present Density Matrix Renormalization Group results for single and coupled cuprate ladders. Our results show that unlike the single-band model, dominant superconducting correlations are not present in the hole doped cuprate ladder. Our coupled ladder calculations show that while the three-band model can explain the quasi-one-dimensional conductivity found in SCCO under ambient pressure, neither increased inter-ladder hopping nor carrier density can explain the dimensional crossover found under pressure prior to superconductivity. We propose that superconductivity in SCCO and other cuprates results can be explained within a valence transition model, following which there is a large increase in carriers on the oxygen sites.   

Quantum Convolutional Neural Network as a Classifier for Many-Body Wavefunctions from the Quantum Variational Eigensolver

Machine learning has been applied on a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems for the identification of phase transitions. The recently proposed quantum convolutional neural network (QCNN) provides a new framework for using quantum circuits instead of classical neural networks as the backbone of classification methods. We present here the results from training the QCNN by the wavefunctions of the variational quantum eigensolver for the one-dimensional transverse field Ising model (TFIM). We demonstrate that the QCNN identifies wavefunctions which correspond to the paramagnetic phase and the ferromagnetic phase of the TFIM with good accuracy. The QCNN can be trained to predict the corresponding phase of wavefunctions around the putative quantum critical point, even though it is trained by wavefunctions far away from it. This provides a basis for exploiting the QCNN to identify the quantum critical point.   

Competing stripe phases in the undoped infinite-layer nickelate

Recent discovery of superconductivity in the nickelates has ignited renewed theoretical and experimental interest in the role of electronic correlations in their properties. In this talk, based on in-depth first-principles and random phase approximation modeling, I will show that the parent (undoped) compound of the nickelate family, LaNiO₂, hosts competing low energy phases, unlike the undoped cuprates but similar to the case of the doped cuprates. In particular, we find charge density wave vectors in agreement with experimental findings. We also show that flat bands near the Fermi level, stemming from the Ni-3dz² orbitals, persist across the various predicted low-energy phases of the nickelates.  Our study gives insight into the microscopic origin of electronic inhomogeneity and the lack of long-range order in nickelates.

 

    

Connections between entanglement entropy and the height field representation for the Fredkin spin chain

The scaling of entanglement entropy with system size has been the focus of intensive, recent study. In particular, there has been significant effort to find physically plausible systems that violate the area law for entanglement entropy. The Fredkin spin chain, proposed by Salberger and Korepin in 2017, is a gapless, frustration-free spin-1/2 system with three-site interactions that violates the area law logarithmically. The height field representation for the ground state provides a simple graphical method to explore properties of the Fredkin spin chain. We present some preliminary results for the height field statistics as a way to understand the entanglement entropy.