Weiguo Yin
One-dimensional systems---ranging from travelling light to circuit cables and from DNA to superstrings---are ubiquitous and critically important to the human knowledge of the universe. However, our engagement with one-dimensional systems in the research and education of spontaneous phase transitions, the phenomena wherein materials can change rapidly between different phases (e.g., gas, liquid, solid, etc.) on their own, has not been largely exercised, since it was proven that one-dimensional systems do not contain phase transitions in the textbook Ising model almost 100 years ago [1] and its quantum counterpart, the Heisenberg model, over 50 years ago [2]. Recently, a spontaneous marginal phase transition (MPT) was discovered in a one-dimensional Ising model containing strong geometrical frustration [3]. Here, by exploring the symmetry of the new mathematical structure underlying the MPT, I report the finding and classification of an infinite number of MPT cases---with highly tunable intriguing behaviors like phase reentrance, the dome shape of transition temperature, pairing, and gauge freedom. These discoveries reveal the possibility of building the MPT-based one-dimensional Ising Machine that can be used to simulate the complex phenomena of phase competition in strongly correlated systems and provide insights with its unambiguous exact solutions. They also form a rich playground for exploring unconventional phase transitions in one-dimensional Heisenberg models.
Niraj Aryal, Xilian Jin, Q. Li, A. M. Tsvelik, Weiguo Yin
We use first-principles methods to reveal that in ZrTe$_5$, a layered van der Waals material like graphite, atomic displacements corresponding to five of the six zone-center A$_g$ (symmetry-preserving) phonon modes can drive a topological phase transition from strong to weak topological insulator with a Dirac semimetal state emerging at the transition, giving rise to a Dirac topology surface in the multi-dimensional space formed by the A$_g$ phonon modes. This implies that the topological phase transition in ZrTe$_5$ can be realized with many different settings of external stimuli that are capable of penetrating through the phonon-space Dirac surface without breaking the crystallographic symmetry. Furthermore, we predict that domains with effective mass of opposite signs can be created by laser pumping and will host Weyl modes of opposite chirality propagating along the domain boundaries. Studying phonon-space topology surfaces provides a new route to understanding and utilizing the exotic physical properties of ZrTe$_5$ and related quantum materials.
Weiguo Yin
The Ising model describes collective behaviors such as phase transitions and critical phenomena in various physical, biological, economical, and social systems. It is well-known that spontaneous phase transition at finite temperature does not exist in the Ising model with short-range interactions in one dimension. Yet, little is known about whether this forbidden phase transition can be approached arbitrarily closely -- at fixed finite temperature. To describe such asymptoticity, here I introduce the notion of marginal phase transition (MPT) and use symmetry analysis of the transfer matrix to reveal the existence of spontaneous MPT at fixed finite temperature $T_0$ in one class of one-dimensional Ising models on decorated two-leg ladders, in which $T_0$ is determined solely by on-rung interactions and decorations, while the crossover width $2δT$ is independently, exponentially reduced ($δT = 0$ means a genuine phase transition) by on-leg interactions and decorations. These findings establish a simple ideal paradigm for realizing an infinite number of one-dimensional Ising systems with spontaneous MPT, which would be characterized in routine lab measurements as a genuine first-order phase transition with large latent heat thanks to the ultra-narrow $δT$ (say less than one nano-kelvin), paving a way to push the limit in our understanding of phase transitions and the dynamical actions of frustration arbitrarily close to the forbidden regime.
Weiguo Yin, A. M. Tsvelik
The prohibition of finite-temperature phase transition in one-dimensional (1D) Ising models and 1D/2D quantum Heisenberg models with short-range interactions fundamentally constrains the application potentials of low-dimensional magnetic materials. Recently, ultranarrow phase crossover (UNPC), which can approach a transition at a desirable finite temperature $T_0$ arbitrarily closely, was discovered in 1D decorated Ising chains and ladders. Here we present a theoretical study of similarly decorated, yet much more challenging, quantum Heisenberg ferrimagnets in a magnetic field, which features ferromagnetic backbone exchange $J$, antiferromagnetic site-decoration coupling $J_{AF}$, and different magnetic moments for the backbone and decorating spins $μ_aS_a<μ_bS_b$. We exactly solved the model in the large $J$ limit -- as a central-macrospin model -- and found two finite-temperature second-order transitions; just above $T_{c2}$ a ``half-ice, half-fire'' regime appears. Finite-$J$ weak-field results follow from an effective-field mapping, suggesting the emergence of UNPC at finite $T_0$ in 2D square lattices thanks to its exponentially strong initial magnetic susceptibility $χ_0\propto e^{4πS_a^2 J/T_0}$, though less likely in 1D chains where $χ_0\propto J/T_0$. These results may shed light on new technological applications of low-dimensional quantum spin systems and attract experimental and computational tests.
Andreas Weichselbaum, Weiguo Yin, Alexei M. Tsvelik
We study the antiferromagnetic spin-half Heisenberg ladder in the presence of an additional frustrating rung spin which is motivated and relevant also for the description of real two-dimensional materials such as the two-dimensional trimer magnet Ba$_4$Ir$_3$O$_{10}$. We study the zero-temperature phase diagram, where we combine numerical and analytical methods into an overall consistent description. All numerical simulations are also accompanied by studies of the dynamical spin structure factor obtained via the density matrix renormalization group. Overall, we find in the regime of strong rung coupling a gapped dimerized phase related to competing symmetry sectors in Hilbert space that ultimately results in frustration-driven spin-Peierls transition. In the weak rung-coupling regime, the system is uniform, yet shows a gapped spinon continuum together with a sharp coherent low-energy branch which renders the system critical overall. In either case, the additional rung spin quickly get sidelined and nearly decouple once their bare coupling to the ladder drops somewhat below the direct Heisenberg coupling of the legs.
Weiguo Yin
OpenAI's reasoning model o3-mini-high was used to carry out an exact analytic study of onedimensional ferrimagnetic site- and bond-decorated q-state Potts models. We demonstrate that the finitetemperature ultranarrow phase crossover (UNPC), driven by a hidden "half-ice, half-fire" state recently discovered in the $q = 2$ case (Ising model), persists for $q > 2$. We identify unique novel features for $q > 2$, including the dome structure in the field-temperature phase diagram and for large $q$ a secondary high-temperature UNPC to the fully disordered paramagnetic state. Moreover, while the crossover temperature $T_0$ in the site-decorated Potts model is independent of the spin interaction $J$ between the backbone spins and thus remains unchanged as the UNPC quickly approaches a genuine transition -- the crossover width is narrowed exponentially -- by enhancing $J$ (referred to as Type-I UNPC), $T_0$ in the bond-decorated Potts model with $q > 2$ depends on $J$ and quickly shifts toward a finite temperature as $J$ increases (referred to as Type-II UNPC). These novel results establish a versatile framework for engineering controlled fast state-flipping switches in low-dimensional systems. Our nine-level AI-contribution rating assigns AI the meritorious status of AI-co-led discovery in this work.
Jackson Lee, Matthew R. Carbone, Weiguo Yin
Understanding charge motion in a background of interacting quantum spins is a fundamental problem in quantum many-body physics. The most extensively studied model for this problem is the so-called $t$-$t'$-$t''$-$J$ model, where the determination of the parameter $t'$ in the context of cuprate superconductors is challenging. Here we present a theoretical study of the spectral functions of a mobile hole in the $t$-$t'$-$t''$-$J$ model using two machine learning techniques: K-nearest Neighbors regression (KNN) and a feed-forward neural network (FFNN). We employ the self-consistent Born approximation to generate a dataset of about $1.3 \times 10^5$ spectral functions. We show that for the forward problem, both methods allow for the accurate and efficient prediction of spectral functions, allowing for e.g. rapid searches through parameter space. Furthermore, we find that for the inverse problem (inferring Hamiltonian parameters from spectra), the FFNN can, but the KNN cannot, accurately predict the model parameters using merely the density-of-state. Our results suggest that it may be possible to use deep learning methods to predict materials parameters from experimentally measured spectral functions.
Weiguo Yin
In a previous paper [Weiguo Yin, Phys. Rev. Res. 6, 013331 (2024)], the forbidden spontaneous phase transition in the one-dimensional Ising model was found to be approachable arbitrarily closely in decorated ladders by ultranarrow phase crossover (UNPC) at a given finite temperature $T_0$ with the crossover width $2δT$ reduced exponentially, which resembles a genuine first-order transition with large latent heat. Here, I reveal that the forbidden phase transition can be approached at fixed $T_0$ as well in decorated single-chain Ising models in the presence of a magnetic field, in which $T_0$ is determined by the interactions involving only the decorated parts and the magnetic field, while $2δT$ is independently, exponentially reduced ($δT=0$ means a genuine transition) by restoring the ferromagnetic interaction between the ordinary spins on the chain backbone -- which was neglected in the previous studies of pseudotransition -- thus manifesting that this asymptoticity to the forbidden transition is essentially the buildup of coherence in preformed crossover of local states. Furthermore, I show that the UNPC can be realized even in the absence of the conventional geometric frustration because the magnetic field itself can induce previously unnoticed hidden spin frustration. These findings make the doors wide open to the engineering and utilization of UNPC as a new paradigm for exploring exotic phenomena and 1D device applications.
Weiguo Yin
The one-dimensional (1D) $J_1$-$J_2$ $q$-state Potts model is solved exactly for arbitrary $q$ by analytically block-diagonalizing the original $q^2\times q^2$ transfer matrix into a simple $2\times 2$ maximally symmetric subspace, based on using OpenAI's reasoning model o3-mini-high to exactly solve the $q=3$ case. Furthermore, by matching relevant subspaces, we map the Potts model onto a simpler effective 1D $q$-state Potts model, where $J_2$ acts as the nearest-neighbor interaction and $J_1$ as an effective magnetic field, nontrivially generalizing a 56-year-old theorem previously limited to the simplest case ($q=2$, the Ising model). Our exact results provide insights to phenomena such as atomic or electronic order stacking in layered materials and the emergence of dome-shaped phases in complex phase diagrams. This work is anticipated to fuel both research in 1D frustrated magnets for recently discovered finite-temperature application potentials and the fast moving topic area of AI in science.
Weiguo Yin
The site-decorated Ising model is introduced to advance the understanding and experimental realization of the recently discovered one-dimensional (1D) finite-temperature ultranarrow phase crossover in an external magnetic field, while mitigating the geometric complexities of traditional bond-decorated models. The unconventional frustration and physics are clarified by exactly mapping the 1D site-decorated Ising model in a magnetic field onto a zero-field bond-decorated $J_1$-$J_2$ Ising model with conventional geometrical frustration. Furthermore, although higher-dimensional Ising models in an external field remain unsolved exactly, an exact solution for a spin-reversal transition -- driven by an exotic, hidden half-ice, half-fire state induced by site decoration -- is derived. This transition, triggered by a slight variation in temperature or magnetic field -- without changing its direction -- even in the weak-field limit, offers a promising route toward energy-efficient applications such as data storage and processing. The results suggest that site decoration offers an avenue for materials and device design, particularly in systems such as mixed $d$-$f$ compounds, optical lattices, and neural networks, calling for further studies with site-decorated Heisenberg models. In addition, the site-decorated model offers a rigorous test ground for artificial intelligence (AI) in science, as the analytic derivation of the present results was not only validated but also improved by a general-purpose large language model, inspiring the use of AI as scientific discoverer.
Niraj Aryal, Xilian Jin, Qiang Li, Mengkun Liu, A. M. Tsvelik, Weiguo Yin
Ultrafast optical control of the structural and electronic properties of various quantum materials has recently sparked great interest. In particular, photoinduced quantum phase transition between distinct topological phases has been considered as a promising route to realize ultrafast topological quantum computers. Here we use first-principles and effective Hamiltonian methods to show that in ZrTe$_5$, a layered topological material, lattice distortions corresponding to all three types of zone-center infrared optical phonon modes can drive the system from the strong or weak topological insulating phase to a Weyl semimetal by breaking the global inversion symmetry. Thus achieved Weyl phases are robust, highly tunable and one of the cleanest ones due to the proximity of the Weyl points to the Fermi level and a lack of other carriers. We further show that the amount of infrared-mode pumping necessary to induce such Weyl phases can be reduced if used in conjunction with an A$_g$ Raman-mode pumping that first drives the system to the Dirac semimetal state. We also find that Berry curvature dipole moment (BCDM), induced by the dynamical inversion symmetry breaking, gives rise to various nonlinear effects that oscillate with the amplitude of the phonon modes. These nonlinear effects present a novel switch for controlling the Weyltronics enabled quantum system.
Weiguo Yin, A. M. Tsvelik
The notion of "half fire, half ice" was recently introduced to describe an exotic macroscopic ground-state degeneracy emerging in a ferrimagnet under the critical magnetic field, in which the "hot" spins are fully disordered on the sublattice with smaller magnetic moments and the "cold" spins are fully ordered on the sublattice with larger magnetic moments. Here we further point out that this state has a twin named "half ice, half fire" in which the hot and cold spins switch positions. The new state is an excited state -- thus hidden in the ground-state phase diagram -- and is robust with respect to the interactions that destroy the half fire, half ice state. We demonstrate with exact results how this hidden state can drive phase switching at desirable finite temperature, even for the one-dimensional Ising model where phase transition at finite temperature is forbidden. We suggest that our findings may open a new door to the understanding and controlling of phase competition and transition in unconventional frustrated systems.
R. J. Koch, R. Sinclair, M. T. McDonnell, R. Yu, M. Abeykoon, M. G. Tucker, A. M. Tsvelik, S. J. L. Billinge, H. D. Zhou, W. -G. Yin, E. S. Bozin
The local structure of NaTiSi$_{2}$O$_{6}$ is examined across its Ti-dimerization orbital-assisted Peierls transition at 210 K. An atomic pair distribution function approach evidences local symmetry breaking preexisting far above the transition. The analysis unravels that on warming the dimers evolve into a short range orbital degeneracy lifted (ODL) state of dual orbital character, persisting up to at least 490 K. The ODL state is correlated over the length scale spanning $\sim$6 sites of the Ti zigzag chains. Results imply that the ODL phenomenology extends to strongly correlated electron systems.
Wei-Guo Yin, Dmitri Volja, Wei Ku
The relative importance of electron-lattice (e-l) and electron-electron (e-e) interactions in ordering orbitals in LaMnO$_3$ is systematically examined within the LDA+$U$ approximation of density functional theory. A realistic effective Hamiltonian is derived from novel Wannier functions analysis of the electronic structure. Surprisingly, e-l interaction ($\simeq 0.9$ eV) alone is found insufficient to stabilize the orbital ordered state. On the other hand, e-e interaction ($\simeq 1.7$ eV) not only induces orbital ordering, but also greatly facilitates the Jahn-Teller distortion via enhanced localization. Further experimental means to quantify the competition between these two mechanisms are proposed.
Wei-Guo Yin, X. Liu, A. M. Tsvelik, M. P. M. Dean, M. H. Upton, Jungho Kim, D. Casa, A. Said, T. Gog, T. F. Qi, G. Cao, J. P. Hill
We report a combined experimental and theoretical study of the unusual ferromagnetism in the one-dimensional copper-iridium oxide Sr$_3$CuIrO$_6$. Utilizing Ir $L_3$ edge resonant inelastic x-ray scattering, we reveal a large gap magnetic excitation spectrum. We find that it is caused by an unusual exchange anisotropy generating mechanism, namely, strong ferromagnetic anisotropy arising from antiferromagnetic superexchange, driven by the alternating strong and weak spin-orbit coupling on the $5d$ Ir and 3d Cu magnetic ions, respectively. From symmetry consideration, this novel mechanism is generally present in systems with edge-sharing Cu$^{2+}$O$_4$ plaquettes and Ir$^{4+}$O$_6$ octahedra. Our results point to unusual magnetic behavior to be expected in mixed 3d-5d transition-metal compounds via exchange pathways that are absent in pure 3d or 5d compounds.
Benjamin A. Frandsen, Emil S. Bozin, Hefei Hu, Yimei Zhu, Yasumasa Nozaki, Hiroshi Kageyama, Yasutomo J. Uemura, Wei-Guo Yin, Simon J. L. Billinge
Understanding the role played by broken symmetry states such as charge, spin, and orbital orders in the mechanism of emergent properties such as high-temperature superconductivity (HTSC) is a major current topic in materials research. That the order may be within one unit cell, such as nematic, was only recently considered theoretically, but its observation in the iron-pnictide and doped cuprate superconductors places it at the forefront of current research. Here we show that the recently discovered BaTi$_2$Sb$_2$O superconductor and its "parent" compound BaTi$_2$As$_2$O form a symmetry-breaking nematic ground state that can be naturally explained as an intra-unit-cell charge order with $d$-wave symmetry, pointing to the ubiquity of the phenomenon. These findings, together with the key structural features in these materials being intermediate between the cuprate and iron-pnictide HTSC materials, render the titanium oxypnictides an important new material system to understand the nature of nematic order and its relationship to superconductivity.
Dmitri Volja, Wei-Guo Yin, Wei Ku
The apparent contradiction between the recently observed weak charge disproportion and the traditional Mn$^{3+}$/Mn$^{4+}$ picture of the charge-orbital orders in half-doped manganites is resolved by a novel Wannier states analysis of the LDA$+U$ electronic structure. Strong electron itinerancy in this charge-transfer system significantly delocalizes the occupied low-energy "Mn$^{3+}$" Wannier states such that charge leaks into the "Mn$^{4+}$"-sites. Furthermore, the leading mechanisms of the charge order are quantified via our first-principles derivation of the low-energy effective Hamiltonian. The electron-electron interaction is found to play a role as important as the electron-lattice interaction. \ignore{A general picture of doped holes in strongly correlated charge-transfer systems is presented and applied to the study of charge order in half-doped manganites, using a novel Wannier states analysis of the LDA$+U$ electronic structure. While residing primarily in the oxygen atoms, the doped holes form additional effective $e_g$ orbitals at the low-energy scale, leading to an effective Mn$^{3+}$/Mn$^{4+}$ valence picture that enables weak charge disproportion, resolving the current serious contradictions between the recent experimental observations of charge distribution and traditional models. Furthermore, the leading mechanisms of the observed charge order are quantified via our first-principles derivation of the low-energy effective Hamiltonian
Wei-Guo Yin, Chia-Hui Lin, Wei Ku
We unveil the novel physical origin of the insulating block checkerboard antiferromagnetism in vacancy-ordered K2Fe4Se5. Our first-principles electronic structure analysis reveals its incompatibility with a simple Fermi-surface nesting or Mott insulator scenario, and suggests the picture of coexisting itinerant and localized electronic states. Consistently, we demonstrate that it can be unified with the metallic collinear or bicollinear antiferromagnetism of the vacancy-free parent compounds LaOFeAs, BaFe2As2, or FeTe in the spin-fermion model. These results indicate that the blocking effects of Hund's rule coupling and the resulting electron correlation are crucial to the electronic and magnetic structures of iron-based superconductors.
Yu Liu, R. J. Koch, Zhixiang Hu, Niraj Aryal, Eli Stavitski, Xiao Tong, Klaus Attenkofer, E. S. Bozin, Weiguo Yin, C. Petrovic
We carried out a comprehensive study of magnetic critical behavior in single crystals of ternary chalcogenide FeCr$_2$Te$_4$ that undergoes a ferrimagnetic transition below $T_c$ $\sim$ 123 K. Detailed critical behavior analysis and scaled magnetic entropy change indicate a second-order ferrimagentic transition. Critical exponents $β= 0.30(1)$ with $T_c = 122.4(5)$ K, $γ= 1.22(1)$ with $T_c = 122.8(1)$ K, and $δ= 4.24(2)$ at $T_c$ $\sim$ 123 K suggest that the spins approach three-dimensional Ising ($β$ = 0.325, $γ$ = 1.24, and $δ$ = 4.82) model coupled with the attractive long-range interactions between spins that decay as $J(r)\approx r^{-4.88}$. Our results suggest that the ferrimagnetism in FeCr$_2$Te$_4$ is due to itinerant ferromagnetism among the antiferromagnetically coupled Cr-Fe-Cr trimers.
Long Yang, Robert J. Koch, Hong Zheng, J. F. Mitchell, Weiguo Yin, Matthew G. Tucker, Simon J. L. Billinge, Emil S. Bozin
The recent discovery of a local fluctuating t2g orbital-degeneracy-lifted (ODL) state in CuIr2S4 as a high temperature precursor to the metal-insulator transition (MIT) opens the door to a possible widespread presence of precursor states in scarcely studied high-temperature regimes of transition metal based quantum materials. Although in CuIr2S4 the ODL state comprises one orbital per Ir, there is no fundamental reason to exclude multi-orbital ODL states in general. The MgTi2O4 spinel exhibits a MIT on cooling at Ts ~250 K, accompanied by Ti t2g orbital ordering (OO) and spin dimerization with the average symmetry reducing to tetragonal. It shares with CuIr2S4 the pyrochlore transition metal sublattice with active t2g orbitals. This, together with its different orbital filling (t2g1 vs t2g5.5) make it a candidate for hosting a multi-orbital ODL precursor state. By combining x-ray and neutron pair distribution function analyses to track the evolution of the local atomic structure across the MIT we find that local tetragonality already exists in the metallic globally cubic phase at high temperature. Local distortions exist up to at least 500 K. Significantly, the high temperature local state is not continuously connected to the OO band insulator ground state, and so the transition cannot be characterized as a trivial order-disorder type. The shortest Ti-Ti spin singlet dimer bonds expand abruptly on warming across the transition but remain shorter than those seen in the cubic structure. These seemingly contradictory observations can be understood within the model of a local fluctuating two-orbital t2g ODL precursor state. The ODL state in MgTi2O4 has a correlation length of about 1 nm at high temperature. We discuss that this extended character of the local distortions is consistent with the two-orbital nature of the ODL state imposed by the charge filling and the bond charge repulsion.