Phase Diagram, $d$-Wave Superconductivity, and Pseudogap of the $t$-$t^{\prime }$-$J$ Model at Finite Temperature

Abstract

Recently, robust $d$-wave superconductive (SC) order has been unveiled in the ground state of the 2D $t$-$t^{\prime }$-$J$ model -- with both nearest-neighbor ($t$) and next-nearest-neighbor ($t^{\prime }$) hoppings -- by density matrix renormalization group studies. However, there is currently a debate on whether the $d$-wave SC holds up strong on both $t^{\prime }/t>0$ and $t^{\prime }/t<0$ cases for the $t$-$t^{\prime }$-$J$ model, which correspond to the electron- and hole-doped sides of the cuprate phase diagram, respectively. Here we exploit state-of-the-art thermal tensor network approach to accurately obtain the phase diagram of the $t$-$t^{\prime }$-$J$ model on cylinders with widths up to $W=6$ and down to low temperature as $T/J\simeq 0.06$, pushing the boundaries of contemporary finite-$T$ calculations. For $t^{\prime }/t>0$, we find a dome-like SC regime with a diverging $d$-wave pairing susceptibility, ${\chi }_{\text{SC}}\propto 1/T^{\alpha }$ below a characteristic temperature $T_c^{\ast }$. Near optimal doping, $T_c^{\ast }$ reaches its highest value of about $0.15J$. Above $T_c^{\ast }$ yet below a higher crossover temperature $T^{\ast }$, the magnetic susceptibility becomes suppressed, which can be related to the onset of pseudogap (PG) behaviors. On the other hand, for $t^{\prime }/t<0$ we find the pairing correlations are much weaker, although there exhibits a node-antinode structure in the PG regime as observed in the hole-doped cuprates. The thermal tensor network calculations of the $t$-$t^{\prime }$-$J$ model underscore both the similarities and differences in the finite-temperature phase diagram between the fundamental model and cuprates, yielding unique insights into their intricate behaviors.

8+8 pages, 4+12 figures

References in corpus (38)

• Theory of Intertwined Orders in High Temperature Superconductors
• The Hubbard Model
• The Hubbard model: A computational perspective
• Minimally Entangled Typical Thermal State Algorithms
• Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs
• Realising the Symmetry-Protected Haldane Phase in Fermi-Hubbard Ladders
• Coexistence of superconductivity with partially filled stripes in the Hubbard model
• Ground State Phase Diagram of the $t$-$t^{\prime }$-$J$ model
• Mott insulating states with competing orders in the triangular lattice Hubbard model
• Linearized Tensor Renormalization Group Algorithm for Thermodynamics of Quantum Lattice Models
• High Temperature Superconductivity in a Lightly Doped Quantum Spin Liquid
• Robust d-wave superconductivity in the square-lattice $t$-$J$ model
• Plaquette versus ordinary $d$-wave pairing in the $t^{\prime }$-Hubbard model on a width 4 cylinder
• Stripes and spin-density waves in the doped two-dimensional Hubbard model: ground state phase diagram
• Magnetically mediated hole pairing in fermionic ladders of ultracold atoms
• Stripes, Antiferromagnetism, and the Pseudogap in the Doped Hubbard Model at Finite Temperature
• Variational tensor network renormalization in imaginary time: benchmark results in the Hubbard model at finite temperature
• Identification of Magnetic Interactions and High-field Quantum Spin Liquid in $\alpha$-RuCl${}_3$
• Effective Hamiltonian for cuprate superconductors derived from multi-scale ab initio scheme with level renormalization
• Tangent Space Approach for Thermal Tensor Network Simulations of the 2D Hubbard Model
• Finite correlation length scaling with infinite projected entangled pair states at finite temperature
• Emergent Superconductivity and Competing Charge Orders in Hole-Doped Square-Lattice $t$-$J$ Model
• Mechanism of Superconductivity in the Hubbard Model at Intermediate Interaction Strength
• Temperature Dependence of Spin and Charge Orders in the Doped Two-Dimensional Hubbard Model
• Hubbard ladders at small $U$ revisited
• Exciton Proliferation and Fate of the Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model
• Thermal Tensor Renormalization Group Simulations of Square-Lattice Quantum Spin Models
• Density-matrix-renormalization-group-based downfolding of the three-band Hubbard model: the importance of density-assisted hopping
• Quantifying the role of antiferromagnetic fluctuations in the superconductivity of the doped Hubbard model
• Universal Thermodynamics in the Kitaev Fractional Liquid
• Quantum Many-Body Simulations of the 2D Fermi-Hubbard Model in Ultracold Optical Lattices
• Superconducting valence bond fluid in lightly doped 8-leg $t$-$J$ cylinders
• Ground-state phase diagram of the extended two-leg $t$-$J$ ladder
• Finite temperature tensor network study of the Hubbard model on an infinite square lattice
• Monte Carlo study of the pseudogap and superconductivity emerging from quantum magnetic fluctuations
• Fragmented Cooper pair condensation in striped superconductors
• Sign structure of the $t$-$t^{\prime }$-$J$ model and its physical consequences
• Learning Effective Spin Hamiltonian of Quantum Magnet

Cited by in corpus (12)

• Accurate Simulation of the Hubbard Model with Finite Fermionic Projected Entangled Pair States
• Quantum Supercritical Regime with Universal Magnetocaloric Scaling in Ising Magnets
• Frustration-Induced Superconductivity in the $t$-$t^{\prime }$ Hubbard Model
• Tunable $t-t^{\prime }-U$ Hubbard models in twisted square homobilayers
• Towards numerically exact computation of conductivity in the thermodynamic limit of interacting lattice models
• Tuning competition between charge order and superconductivity in the square-lattice $t$-$t^{\prime }$-$J$ model
• Thermal Tensor Network Simulations of Lattice Fermions with Fixed Filling
• Finite temperature dopant-induced spin reorganization explored via tensor networks in the two-dimensional $t$-$J$ model
• Strengthened correlations near [110] edges of $d$-wave superconductors in the t-J model with the Gutzwiller approximation
• Nonpertubative Many-Body Theory for the Two-Dimensional Hubbard Model at Low Temperature: From Weak to Strong Coupling Regimes
• Spinon Singlet Pairing: Origin of $d$-Wave Sign Structure in a Partially-Filled Stripe
• Probing Non-Fermi-Liquid Behaviour of Composite Fermi Liquid via Efficient Thermal Simulations