Pub Date : 2020-10-13DOI: 10.1103/PHYSREVRESEARCH.3.023054
P. Lunts, A. Georges, E. Stoudenmire, M. Fishman
We numerically solve the Hubbard model on the Bethe lattice with finite coordination number $z=3$, and determine its zero-temperature phase diagram. For this purpose, we introduce and develop the `variational uniform tree state' (VUTS) algorithm, a tensor network algorithm which generalizes the variational uniform matrix product state algorithm to tree tensor networks. Our results reveal an antiferromagnetic insulating phase and a paramagnetic metallic phase, separated by a first-order doping-driven metal-insulator transition. We show that the metallic state is a Fermi liquid with coherent quasiparticle excitations for all values of the interaction strength $U$, and we obtain the finite quasiparticle weight $Z$ from the single-particle occupation function of a generalized "momentum" variable. We find that $Z$ decreases with increasing $U$, ultimately saturating to a non-zero, doping-dependent value. Our work demonstrates that tensor-network calculations on tree lattices, and the VUTS algorithm in particular, are a platform for obtaining controlled results for phenomena absent in one dimension, such as Fermi liquids, while avoiding computational difficulties associated with tensor networks in two dimensions. We envision that future studies could observe non-Fermi liquids, interaction-driven metal-insulator transitions, and doped spin liquids using this platform.
{"title":"Hubbard model on the Bethe lattice via variational uniform tree states: Metal-insulator transition and a Fermi liquid","authors":"P. Lunts, A. Georges, E. Stoudenmire, M. Fishman","doi":"10.1103/PHYSREVRESEARCH.3.023054","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.3.023054","url":null,"abstract":"We numerically solve the Hubbard model on the Bethe lattice with finite coordination number $z=3$, and determine its zero-temperature phase diagram. For this purpose, we introduce and develop the `variational uniform tree state' (VUTS) algorithm, a tensor network algorithm which generalizes the variational uniform matrix product state algorithm to tree tensor networks. Our results reveal an antiferromagnetic insulating phase and a paramagnetic metallic phase, separated by a first-order doping-driven metal-insulator transition. We show that the metallic state is a Fermi liquid with coherent quasiparticle excitations for all values of the interaction strength $U$, and we obtain the finite quasiparticle weight $Z$ from the single-particle occupation function of a generalized \"momentum\" variable. We find that $Z$ decreases with increasing $U$, ultimately saturating to a non-zero, doping-dependent value. Our work demonstrates that tensor-network calculations on tree lattices, and the VUTS algorithm in particular, are a platform for obtaining controlled results for phenomena absent in one dimension, such as Fermi liquids, while avoiding computational difficulties associated with tensor networks in two dimensions. We envision that future studies could observe non-Fermi liquids, interaction-driven metal-insulator transitions, and doped spin liquids using this platform.","PeriodicalId":8511,"journal":{"name":"arXiv: Strongly Correlated Electrons","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84592257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-13DOI: 10.1103/PHYSREVMATERIALS.5.015001
I. Kurata, J. A. Flores-Livas, H. Sugimoto, H. Takahashi, H. Sagayama, Y. Yamasaki, T. Nomoto, R. Arita, S. Ishiwata
A new layered perovskite-type oxide Ba$_2$RhO$_4$ was synthesized by a high-pressure technique with the support of convex-hull calculations. The crystal and electronic structure were studied by both experimental and computational tools. Structural refinements for powder x-ray diffraction data showed that Ba$_2$RhO$_4$ crystallizes in a K$_2$NiF$_4$-type structure, isostructural to Sr$_2$RuO$_4$ and Ba$_2$IrO$_4$. Magnetic, resistivity, and specific heat measurements for polycrystalline samples of Ba$_2$RhO$_4$ indicate that the system can be characterized as a correlated metal. Despite the close similarity to its Sr$_2$RuO$_4$ counterpart in the electronic specific heat coefficient and the Wilson ratio, Ba$_2$RhO$_4$ shows no signature of superconductivity down to 0.16 K. Whereas the Fermi surface topology has reminiscent pieces of Sr$_2$RuO$_4$, an electron-like e$_g$-($d_{x^2-y^2}$) band descends below the Fermi level, making of this compound unique also as a metallic counterpart of the spin-orbit-coupled Mott insulator Ba$_2$IrO$_4$.
{"title":"High-pressure synthesis of \u0000Ba2RhO4\u0000, a rhodate analog of the layered perovskite Sr-ruthenate","authors":"I. Kurata, J. A. Flores-Livas, H. Sugimoto, H. Takahashi, H. Sagayama, Y. Yamasaki, T. Nomoto, R. Arita, S. Ishiwata","doi":"10.1103/PHYSREVMATERIALS.5.015001","DOIUrl":"https://doi.org/10.1103/PHYSREVMATERIALS.5.015001","url":null,"abstract":"A new layered perovskite-type oxide Ba$_2$RhO$_4$ was synthesized by a high-pressure technique with the support of convex-hull calculations. The crystal and electronic structure were studied by both experimental and computational tools. Structural refinements for powder x-ray diffraction data showed that Ba$_2$RhO$_4$ crystallizes in a K$_2$NiF$_4$-type structure, isostructural to Sr$_2$RuO$_4$ and Ba$_2$IrO$_4$. Magnetic, resistivity, and specific heat measurements for polycrystalline samples of Ba$_2$RhO$_4$ indicate that the system can be characterized as a correlated metal. Despite the close similarity to its Sr$_2$RuO$_4$ counterpart in the electronic specific heat coefficient and the Wilson ratio, Ba$_2$RhO$_4$ shows no signature of superconductivity down to 0.16 K. Whereas the Fermi surface topology has reminiscent pieces of Sr$_2$RuO$_4$, an electron-like e$_g$-($d_{x^2-y^2}$) band descends below the Fermi level, making of this compound unique also as a metallic counterpart of the spin-orbit-coupled Mott insulator Ba$_2$IrO$_4$.","PeriodicalId":8511,"journal":{"name":"arXiv: Strongly Correlated Electrons","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81238659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}