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arXiv:2606.16968

Electronic Green's function across the pseudogap to stripe transition in the $t$-$t'$-$J$ model

Martin Ulaga, Aritra Sinha, Alexander Wietek

Published Jun 15, 2026• 0 citations
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Abstract

Superconducting domes in strongly correlated electronic systems are often accompanied by charge density waves and peculiar features in the electronic structure. The appearance of a pseudogap, in particular, and its relation to charge density waves remains insufficiently understood. Here, we investigate the electronic Green's function of the underdoped $t$-$t'$-$J$ model of the cuprate superconductors using tensor network algorithms for finite temperature dynamics on cylinders of width $4$. We find the prominent momentum differentiation, the hallmark of the pseudogap, to be strongly dependent on $t'$, which develops into a momentum-dependent opening of a gap upon decreasing temperature, consistent with the formation of a Fermi arc at intermediate temperatures. The nodal gap around ${\bf k}=(π/2,π/2)$ closes and fills with increasing temperature as coherent stripe order melts into a regime of fluctuating charge clusters.

DOI
10.48550/arxiv.2606.16968

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Electronic Green's function across the pseudogap to stripe transition in the ttt-t′t't′-JJJ model
Superconducting domes in strongly correlated electronic systems are often accompanied by charge density waves and peculiar features in the electronic structure. The appearance of a pseudogap, in particular, and its relation to charge density waves remains insufficiently understood. Here, we investigate the electronic Green's function of the underdoped ttt-t′t't′-JJJ model of the cuprate superconductors using tensor network algorithms for finite temperature dynamics on cylinders of width 444. We find the prominent momentum differentiation, the hallmark of the pseudogap, to be strongly dependent on t′t't′, which develops into a momentum-dependent opening of a gap upon decreasing temperature, consistent with the formation of a Fermi arc at intermediate temperatures. The nodal gap around k=(π/2,π/2){\bf k}=(π/2,π/2)k=(π/2,π/2) closes and fills with increasing temperature as coherent stripe order melts into a regime of fluctuating charge clusters.
We study the electronic structure within a system of phase-decoupled one-dimensional superconductors coexisting with stripe spin and charge-density-wave order. This system has a nodal Fermi surface (Fermi arc) in the form of a hole pocket and an antinodal pseudogap. The spectral function in the antinodes is approximately particle-hole symmetric contrary to the gapped regions just outside the pocket. We find that states at the Fermi energy are extended whereas states near the pseudogap energy have localization lengths as short as the interstripe spacing. We consider pairing which has either local ddd-wave or sss-wave symmetry and find similar results in both cases, consistent with the pseudogap being an effect of local pair correlations. We suggest that this state is a stripe-ordered caricature of the pseudogap phase in underdoped cuprates with coexisting spin-, charge-, and pair-density-wave correlations. Lastly, we also model a superconducting state which (1) evolves smoothly from the pseudogap state, (2) has a signature subgap peak in the density of states, and (3) has the coherent pair density concentrated to the nodal region.
Evolution of superconductivity from charge clusters to stripes in the ttt-t′t't′-JJJ model
Competition and coexistence of charge orders and superconductivity are hallmarks in many strongly correlated electron systems. Here, we unravel the precise role of charge fluctuations on the superconducting state in the ttt-t′t't′-JJJ model of the high-temperature cuprate superconductors. Using finite-temperature tensor network simulations, we investigate thermal snapshots in the underdoped regime where the ground state features a superconducting stripe phase. At intermediate temperatures, where stripes have melted and hole clustering is observed, we find that pairing correlations are tightly localized on the hole clusters. Upon entering the stripe regime at lower temperatures, pairing increasingly delocalizes across different hole clusters to ultimately become coherent across the full system in the ground state. This pair-charge locking gives rise to an intuitive picture of the parent state of the superconducting stripe phase: pairing is localized on hole clusters formed via hole attraction due to the onset of magnetic correlations at intermediate temperature. We discuss how this microscopic picture is consistent with a broad range of experimental observations in cuprate superconductors, including scanning tunneling microscopy (STM) evidence for local pairing above TcT_cTc​ and nuclear magnetic resonance (NMR) signatures of charge clustering in the underdoped regime.
We study electronic structure of hole- and electron-doped Mott insulators in the two-dimensional Hubbard model to reach a unified picture for the normal state of cuprate high-Tc{T}_{c}Tc​ superconductors. By using a cluster extension of the dynamical mean-field theory, we demonstrate that structure of coexisting zeros and poles of the single-particle Green's function holds the key to understand Mott physics in the underdoped region. We show evidence for the emergence of non-Fermi-liquid phase caused by the topological quantum phase transition of Fermi surface by analyzing low-energy charge dynamics. The spectra calculated in a wide range of energy and momentum reproduce various anomalous properties observed in experiments for the high-Tc{T}_{c}Tc​ cuprates. Our results reveal that the pseudogap in hole-doped cuprates has a ddd-wavelike structure only below the Fermi level while it retains non-ddd-wave structure with a fully opened gap above the Fermi energy even in the nodal direction due to a zero surface extending over the entire Brillouin zone. In addition to the non-ddd-wave pseudogap, the present comprehensive identifications of the spectral asymmetry as to the Fermi energy, the Fermi arc, and the back-bending behavior of the dispersion, waterfall, and low-energy kink, in agreement with the experimental anomalies of the cuprates, do not support that these originate from (the precursors of) symmetry breakings such as the preformed pairing and the ddd-density-wave fluctuations, but support that they are direct consequences of the proximity to the Mott insulator. Several possible experiments are further proposed to prove or disprove our zero mechanism.
Stripe order is a prominent feature in the phase diagram of the cuprate superconductors and has been established as the lowest-energy state of the two-dimensional Fermi-Hubbard model in relevant regimes. As temperature rises, stripes and superconductivity give way to the interesting strange-metal and pseudogap regimes. Here we investigate a crucial aspect of these regimes using numerical simulations of the square lattice Hubbard model. Using infinite projected entangled pair states with purification in the thermodynamic limit, we show that the thermodynamic charge susceptibility develops a broad maximum above the stripe regime at filling near n = 0.90, that strengthens upon cooling. Minimally entangled typical thermal states on finite cylinders attribute this enhancement to the emergence of large, fluctuating charge clusters, while the charge susceptibility remains finite. Upon further cooling, the cluster sizes stop broadening and lock to the stripe wavelength, indicating that interaction-driven clustering organizes the intermediate-temperature landscape but is ultimately forestalled by stripe order at low temperature.
Fluctuating Pair Density Wave in Finite-temperature Phase Diagram of the ttt-t′t^\primet′ Hubbard Model
The Hubbard model and its extensions are canonical theoretical frameworks for understanding correlated electronic states, including those in high-TcT_cTc​ cuprates. Here, we use state-of-the-art thermal tensor network method to map out the temperature-doping phase diagram of the ttt-t′t^\primet′ Hubbard model. On the electron-doped side, we find a ddd-wave superconducting (dSC) regime, supporting the scenario of high-TcT_cTc​ superconductivity. In contrast, on the hole-doped side, no robust dSC phase is detected. Instead, a finite-temperature regime dominated by strong pair-density-wave (PDW) fluctuations emerges, which may eventually give way to charge density wave order upon further cooling. The PDW state exhibits inter-arc pairing with net momentum near (0,π)(0, π)(0,π), distinct from the zero-momentum pairing in conventional dSC. Furthermore, these fluctuating PDW states occupy the lower portion of the pseudogap regime on the hole-doped side. We provide a comprehensive finite-temperature perspective consistent with previous ground-state studies, shedding new light on pairing instabilities and exotic electronic states in high-TcT_cTc​ superconductors.
Using an exact diagonalization method within the dynamical mean-field theory we analyze the stable stripe structures found in the two-dimensional Hubbard model doped by $0.03<\ensuremath{\delta}<0.2$ holes, and discuss a scenario for stripe melting. Our results demonstrate the importance of dynamical correlations which lead to the metallic stripes, in contrast to the Hartree-Fock picture. The spectral functions show a coexistence of the coherent quasiparticles (polaron band) close to the Fermi energy \ensuremath{\mu}, and incoherent states at lower energies. The quasiparticles in the polaron band depend on hole doping, and hybridize strongly with the partly filled mid-gap band within the Mott-Hubbard gap, induced by stripe order. This explains the origin of nondispersive quasiparticles close to the Fermi energy \ensuremath{\mu}, observed near the $X=(\ensuremath{\pi},0)$ and $Y=(0,\ensuremath{\pi})$ points for the samples with coexisting (10) and (01) stripes. We reproduce the gap which opens for charge excitations at the $S=(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ point, observed in the angle-resolved photoemission experiments for ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4},$ and a pseudogap in the integrated spectral density pinned to \ensuremath{\mu}. Finally, we show that large spectral weight close to $\ensuremath{\mu}$ moves from the X to the S point when the second neighbor hopping element increases, and the (01) stripe phase is destabilized by kink fluctuations.