Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes

Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and the lack of a general framework for classifications. While frustration-free Hamiltonians, which appear as fixed point Hamiltonians of renormalization group transformations, may serve as representatives of quantum phases, it is still difficult to analyze and classify quantum phases of arbitrary frustration-free Hamiltonians exhaustively. Here, we address these problems by sharpening our considerations to a certain subclass of frustration-free Hamiltonians, called stabilizer Hamiltonians, which have been actively studied in quantum information science. We propose a model of frustration-free Hamiltonians which covers a large class of physically realistic stabilizer Hamiltonians, constrained to only three physical conditions; the locality of interaction terms, translation symmetries and scale symmetries, meaning that the number of ground states does not grow with the system size. We show that quantum phases arising in two-dimensional models can be classified exactly through certain quantum coding theoretical operators, called logical operators, by proving that two models with topologically distinct shapes of logical operators are always separated by quantum phase transitions.     

Aberrated diffraction patterns of off-axis Gaussian beams

Fraunhofer diffraction patterns of off-axis Gaussian beams passing through an optical system having primary spherical aberration are investigated. The resultant diffraction patterns show a nearly elliptical form with a transverse focal shift which depends on the incident position of the Gaussian beams on the pupil and on their radius.     

57Fe and57Co Mössbauer studies of highT c Y-Ba-Cu oxides

The⁵⁷Co emission Mössbauer spectra from YBa₂Cu₃O_6.92 (1-2-307) and YBa₂Cu₃O_6.00 (1-2-306) have been measured and compared with the⁵⁷Fe absorption spectra from YBa₂Cu_2.95Fe_0.05O_7?δ in order to clarify decisively the site assignments for the⁵⁷Fe quadrupole-split doublets in these compounds. Mössbauer spectra obtained from both specimens consist of four components whose hyperfine interaction parameters well agree with each other. It is shown that the Co and Fe atoms mainly substitute at Cu1 chain sites in 1-2-307, but in 1-2-306 the Co atoms occupy randomly the Cu2 plane sites and indicate magnetically-split sextet which converts to a paramagnetic doublet of S-state Fe³⁺ in 1-2-307 by a post-annealing in O₂ gas.     

Resonance Raman effect in thiourea

Raman spectra of thiourea have been observed in H₂O and D₂O solutions with the exciting laser beams of 514.5, 488.0, 457.9, 363.8, 325.0, and 257.3 nm. The resonance Raman excitation profile of the 729-cm^?1 line has been examined in the region of the 237-nm absorption band ($\text{π}{}_{\mathrm{<mtext>CS</mtext>}}{}^1\text{← π}{}_{\mathrm{<mtext>CS</mtext>}}$) by use of a solvent shift of the absorption band instead of by changing the wavelength of the exciting beam. The depolarization degree of this line was measured and its overtone Raman line was also observed. On the basis of the results of these experiments, it has been concluded that the 729-cm^?1 Raman line, assignable to the CS stretching vibration, derives its intensity solely from the 237-nm band when it is excited at 257.3 or 325.0 nm. On exciting in the region 363.8–514.5 nm, however, contributions of the higher-frequency bands are predominant rather than the contribution from the 237-nm band. The Raman line at 1520 cm^?1 of thiourea-d₄ is assignable to the NCN antisymmetric stretching vibration. From its excitation profile, its intensity has been considered to come from a vibronic coupling between the excited electronic states of the 220-nm ($\text{π}{}_{\mathrm{<mtext>CS</mtext>}}{}^1\text{← π}{}_{\mathrm{<mtext>N</mtext>}}\text{? π}{}_{\mathrm{<mtext>N</mtext>}}$) and the 197-nm ($\text{π}{}_{\mathrm{<mtext>CS</mtext>}}{}^1\text{← π}{}_{\mathrm{<mtext>N</mtext>}}\text{+ π}{}_{\mathrm{<mtext>N</mtext>}}$) bands.     

Phase transitions in N—n-propylpyridinium-TCNQ2 and N—n-butylpyridinium-TCNQn at high pressures

The electrical resistivity of N-n-propylpyridinium-TCNQ₂ (NPPy-TCNQ₂) and N-n-butylpyridinium-TCNQ_n (NBPy-TCNQ_n) has been measured as a function of temperature and pressure. Phase transitions in these salts have been studied at high pressures. The transition temperature (T_c) in NPPy-TCNQ₂ at atmospheric pressure increased with increasing pressure at the rate of dT_c/dP = + 12.0 degkbar^?1. The value of volume change calculated from the Clapeylon-Clausius relation was + 4.4 cm³ mol^?1. The electrical resistivity along the a- and c-axis increased with increasing pressure below 7 kbar. This anomalous electrical behaviour is closely related to the crystal structure of NPPy-TCNQ₂. The resistivity dropped sharply at about 11 kbar. This abrupt change may be due to a new pressure induced phase transition.The T_c of the NBPy-TCNQ_n increased remarkably with increasing pressure up to 0.7 kbar, above which the phase transition disappeared. The phase transitions of N-n-alkyl-substituted pyridinium TCNQ salts depend strongly on the nature of cations.     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

Magnetic resonance in a [{Cr(CN)<Subscript>6</Subscript>} {Mn(S)-<Emphasis Type="Italic">pn</Emphasis>H-(H<Subscript>2</Subscript>O)}] · H<Subscript>2</Subscript>O single-crystal molecular ferrimagnet

The variations in the magnetic resonance spectra accompanying the transition from the paramagnetic to ferrimagnetic state in [{Cr(CN)₆} {Mn(S)-pnH-(H₂O) }] · H₂O orthorhombic chiral molecular crystals were studied. The dependence of the EPR linewidth on temperature in the proximity of the transition point T_C = 38 K argues for the two-dimensional character of spin ordering. The spin resonance line was found to undergo exchange narrowing at T > T_C. The ferrimagnetic phase has an easy magnetization axis coinciding with the a crystallographic axis.